wave optics formulas pyqs

Complete Formula Sheet

Basic wave relation

v = fλn = c/vOptical path = nℓ

Wavefront geometry

Point source → spherical wavefrontLine source → cylindrical wavefrontDistant source → plane wavefront

Huygens principle

Wavelet radius = vtNew wavefront = forward envelope

Reflection

i = rIncident and reflected wavefronts remain perpendicular to rays

Refraction

sin i / sin r = v₁/v₂ = n₂/n₁n₁ sin i = n₂ sin r

Doppler light shift

For v ≪ c: Δλ/λ ≈ v/cRed shift: source recedes

Path and phase

Δ = path differenceφ = (2π/λ)ΔΔ = φλ/(2π)

Bright and dark

Bright: Δ = nλ, φ = 2nπDark: Δ = (2n−1)λ/2, φ = (2n−1)π

General intensity

I = I₁ + I₂ + 2√(I₁I₂)cosφImax = (√I₁+√I₂)²Imin = (√I₁−√I₂)²

Equal intensities

I = 4I₀cos²(φ/2)Imax = 4I₀Imin = 0

Visibility

V = (Imax−Imin)/(Imax+Imin)V = 2√(I₁I₂)/(I₁+I₂)

Geometry

Δ = xd/Dβ = λD/dAngular fringe width = λ/d

Fringe positions

Bright: xₙ = nβDark: xₙ = (2n−1)β/2

Thin sheet

Additional path Δp = (μ−1)tFringe shift Δx = D(μ−1)t/dΔx = β(μ−1)t/λ

Liquid

λ′ = λ/μβ′ = β/μ

Source and screen shift

Source shift: pattern shifts, β unchangedScreen shift: β changes with D

Missing orders

Interference maximum: d sinθ = nλDiffraction minimum: a sinθ = mλMissing order: n = m(d/a)

Single slit

Δ = a sinθMinima: a sinθ = nλFor small θ: θₙ ≈ nλ/a

Secondary maxima

Approx.: a sinθ ≈ (2n+1)λ/2Exact: tanα = α, α = πa sinθ/λ

Central maximum

Angular width = 2λ/aLinear width = 2Dλ/a

Resolution

Telescope: θmin = 1.22λ/DResolving power of grating: RP = λ/Δλ = mNMicroscope: dmin ≈ 0.61λ/NA

Unpolarised light

After ideal polariser: I = I₀/2Polarisation proves transverse nature

Malus law

I = Iₚcos²θCrossed polarisers: θ = 90°, I = 0

Brewster law

μ = tan iₚiₚ + r = 90°

Degree of polarisation

P = (Imax−Imin)/(Imax+Imin)

Wavefront Formulae

Basic wave relation

v = fλn = c/vOptical path = nℓ

Wavefront geometry

Point source → spherical wavefrontLine source → cylindrical wavefrontDistant source → plane wavefront

Huygens principle

Wavelet radius = vtNew wavefront = forward envelope

Reflection

i = rIncident and reflected wavefronts remain perpendicular to rays

Refraction

sin i / sin r = v₁/v₂ = n₂/n₁n₁ sin i = n₂ sin r

Doppler light shift

For v ≪ c: Δλ/λ ≈ v/cRed shift: source recedes

Interference Formulae

Path and phase

Δ = path differenceφ = (2π/λ)ΔΔ = φλ/(2π)

Bright and dark

Bright: Δ = nλ, φ = 2nπDark: Δ = (2n−1)λ/2, φ = (2n−1)π

General intensity

I = I₁ + I₂ + 2√(I₁I₂)cosφImax = (√I₁+√I₂)²Imin = (√I₁−√I₂)²

Equal intensities

I = 4I₀cos²(φ/2)Imax = 4I₀Imin = 0

Visibility

V = (Imax−Imin)/(Imax+Imin)V = 2√(I₁I₂)/(I₁+I₂)

YDSE Formulae

Geometry

Δ = xd/Dβ = λD/dAngular fringe width = λ/d

Fringe positions

Bright: xₙ = nβDark: xₙ = (2n−1)β/2

Thin sheet

Additional path Δp = (μ−1)tFringe shift Δx = D(μ−1)t/dΔx = β(μ−1)t/λ

Liquid

λ′ = λ/μβ′ = β/μ

Source and screen shift

Source shift: pattern shifts, β unchangedScreen shift: β changes with D

Missing orders

Interference maximum: d sinθ = nλDiffraction minimum: a sinθ = mλMissing order: n = m(d/a)

Diffraction Formulae

Single slit

Δ = a sinθMinima: a sinθ = nλFor small θ: θₙ ≈ nλ/a

Secondary maxima

Approx.: a sinθ ≈ (2n+1)λ/2Exact: tanα = α, α = πa sinθ/λ

Central maximum

Angular width = 2λ/aLinear width = 2Dλ/a

Resolution

Telescope: θmin = 1.22λ/DResolving power of grating: RP = λ/Δλ = mNMicroscope: dmin ≈ 0.61λ/NA

Polarisation Formulae

Unpolarised light

After ideal polariser: I = I₀/2Polarisation proves transverse nature

Malus law

I = Iₚcos²θCrossed polarisers: θ = 90°, I = 0

Brewster law

μ = tan iₚiₚ + r = 90°

Degree of polarisation

P = (Imax−Imin)/(Imax+Imin)

Malus Law Formulae

Malus Law

I = Iₚcos²θθ = angle between transmission axesCrossed axes → I = 0

For initially unpolarised intensity I₀, the first ideal polariser gives Iₚ = I₀/2; an analyser then gives I = (I₀/2)cos²θ.

Brewster Law Formulae

Brewster Law

μ = tan iₚiₚ + r = 90°Reflected beam is completely plane-polarised at iₚ

The reflected and refracted rays are perpendicular at the polarising angle.

NCERT Examples · Complete Paraphrased Solutions

Questions are concisely paraphrased from the supplied references; solutions and calculations are original.

NCERT 10.1

Paraphrased question: A 589 nm monochromatic wave enters water of refractive index 1.33. Determine reflected and transmitted wavelength, frequency and speed.

Reflection remains in air: λᵣ = 589 nm, vᵣ ≈ 3.00×10⁸ m s⁻¹. Frequency is fixed by the source: f = c/λ = 3.00×10⁸/(589×10⁻⁹) ≈ 5.09×10¹⁴ Hz. In water, v = c/n ≈ 2.26×10⁸ m s⁻¹ and λ′ = λ/n ≈ 443 nm. Frequency remains 5.09×10¹⁴ Hz.

NCERT 10.2

Paraphrased question: Identify the wavefront shape for a point source, light emerging from a convex lens with the source at its focus, and light from a very distant star.

A point source produces a spherical wavefront. A point at the focus of a convex lens produces parallel emerging rays, hence a plane wavefront. The small portion of a stellar spherical wavefront reaching Earth is effectively plane.

Wavefront shapes used in NCERT wave-optics reasoning.

NCERT 10.3

Paraphrased question: For glass of refractive index 1.5, determine light speed and discuss colour dependence.

v = c/n = 3.00×10⁸/1.5 = 2.00×10⁸ m s⁻¹. In dispersive glass, n depends on wavelength; violet generally has larger n and travels more slowly than red.

NCERT 10.4

Paraphrased question: In YDSE, d = 0.28 mm, D = 1.4 m and the fourth bright fringe is 1.2 cm from the centre. Find λ.

x₄ = 4λD/d. Therefore λ = x₄d/(4D) = (0.012)(0.28×10⁻³)/(4×1.4) = 6.0×10⁻⁷ m = 600 nm.

NCERT 10.5

Paraphrased question: Equal-beam interference has intensity K at path difference λ. Find intensity at path difference λ/3.

At Δ = λ, φ = 2π and K = Imax = 4I₀. At Δ = λ/3, φ = 2π/3. I = 4I₀cos²(π/3) = I₀ = K/4.

NCERT 10.6

Paraphrased question: Two wavelengths, 650 nm and 520 nm, form YDSE fringes. Relate the third 650 nm bright position and find the first common bright order.

For 650 nm, x₃ = 3(650 nm)D/d = 1950 nm·D/d. Coincidence requires m(650)=n(520), so 5m=4n. The least integers are m=4 and n=5; common position = 2600 nm·D/d.

NCERT 10.11

Paraphrased question: A 656.3 nm hydrogen line is red-shifted by 1.5 nm. Estimate recession speed.

For v ≪ c, v/c = Δλ/λ. Thus v = 3.00×10⁸(1.5/656.3) ≈ 6.86×10⁵ m s⁻¹, directed away from Earth.

NCERT 10.12

Paraphrased question: Compare the corpuscular prediction for light speed in water with experiment.

The old corpuscular picture predicted acceleration into a denser medium. Measurements show light slows in water. The wave description, with v = c/n, agrees with experiment.

NCERT 10.13

Paraphrased question: Use Huygens construction to explain why a plane mirror forms a virtual image at equal distance behind it.

Each reflected wavefront obeys i = r. Backward extensions of the reflected normals meet symmetrically behind the mirror. Equal-angle geometry gives image distance = object distance, with the image virtual.

NCERT 10.14

Paraphrased question: Which listed factors affect wave speed in vacuum and in a material medium?

In vacuum, c is invariant and independent of source nature, direction, source/observer motion, wavelength and intensity. In a material, speed depends mainly on the medium and generally on wavelength through dispersion; in ordinary linear media it is not set by intensity or source motion.

NCERT 10.15

Paraphrased question: Why are source-motion and observer-motion Doppler expressions symmetric for light in vacuum?

Vacuum provides no preferred mechanical medium. Special relativity makes relative motion the relevant quantity. In a material medium, the medium defines a preferred frame, so the symmetry need not hold in the same simple form.

NCERT 10.16

Paraphrased question: YDSE uses λ = 600 nm and angular fringe width 0.1°. Find slit spacing.

Angular width = λ/d. Convert 0.1° = 1.745×10⁻³ rad. Hence d = 600×10⁻⁹/(1.745×10⁻³) ≈ 3.44×10⁻⁴ m = 0.344 mm.

NCERT 10.17

Paraphrased question: Explain aperture doubling, diffraction envelope in YDSE, Poisson spot, sound around a wall, and why ray optics remains useful.

Doubling slit width halves central-band width and increases collected amplitude, raising central intensity. Each YDSE slit diffracts, so interference fringes lie inside a single-slit envelope. A circular obstacle sends equal-phase edge wavelets to the axis, creating a bright Poisson spot. Sound bends strongly because its wavelength is comparable with room dimensions, unlike light. Ray optics remains an excellent approximation whenever apertures and objects are much larger than λ.

NCERT 10.18

Paraphrased question: Two towers are 40 km apart; the straight joining line clears a ridge by 50 m. Estimate the longest radio wavelength with negligible diffraction.

Using the Fresnel-scale estimate √(λD) ≪ clearance, take λD ≲ h². With D = 4.0×10⁴ m and h = 50 m, λ ≲ h²/D = 2500/40000 ≈ 6.25×10⁻² m. For truly negligible diffraction one chooses appreciably below about 6 cm.

NCERT 10.19

Paraphrased question: For λ = 500 nm, screen distance 1 m and first minimum 2.5 mm from centre, find slit width.

First minimum y₁ = Dλ/a. Thus a = Dλ/y₁ = (1)(500×10⁻⁹)/(2.5×10⁻³) = 2.0×10⁻⁴ m = 0.20 mm.

NCERT 10.20

Paraphrased question: Explain aircraft-induced TV picture fluctuations and justify linear superposition.

A moving aircraft reflects a delayed radio/TV signal; its changing path creates time-varying interference at the receiver. Linear superposition follows because Maxwell's equations are linear in ordinary media, so the sum of individual field solutions is also a solution.

NCERT 10.21

Paraphrased question: Show by slit subdivision why intensity vanishes at a sinθ = nλ.

For a sinθ = nλ, divide the slit into 2n equal strips. The path difference between corresponding points in adjacent paired strips is λ/2, giving phase difference π. Every pair cancels, so resultant amplitude and intensity are zero.

CBSE Questions

CBSE Question Bank · 60 Questions

25 MCQs

M1In CBSE style, select the correct result for wavefront normal.

A. is parallel to ray direction

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. is parallel to ray direction

Detailed solution: The governing wave-optics result is is parallel to ray direction.

M2In CBSE style, select the correct result for Snell law.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. n₁sin i = n₂sin r

Answer: D. n₁sin i = n₂sin r

Detailed solution: The governing wave-optics result is n₁sin i = n₂sin r.

M3In CBSE style, select the correct result for bright interference.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. Δ = nλ

D. frequency always changes

Answer: C. Δ = nλ

Detailed solution: The governing wave-optics result is Δ = nλ.

M4In CBSE style, select the correct result for dark interference.

A. path difference equals phase difference

B. Δ = (2n−1)λ/2

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. Δ = (2n−1)λ/2

Detailed solution: The governing wave-optics result is Δ = (2n−1)λ/2.

M5In CBSE style, select the correct result for phase relation.

A. φ = 2πΔ/λ

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. φ = 2πΔ/λ

Detailed solution: The governing wave-optics result is φ = 2πΔ/λ.

M6In CBSE style, select the correct result for YDSE fringe width.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. β = λD/d

Answer: D. β = λD/d

Detailed solution: The governing wave-optics result is β = λD/d.

M7In CBSE style, select the correct result for thin-sheet shift.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. Δx = D(μ−1)t/d

D. frequency always changes

Answer: C. Δx = D(μ−1)t/d

Detailed solution: The governing wave-optics result is Δx = D(μ−1)t/d.

M8In CBSE style, select the correct result for liquid immersion.

A. path difference equals phase difference

B. β′ = β/μ

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. β′ = β/μ

Detailed solution: The governing wave-optics result is β′ = β/μ.

M9In CBSE style, select the correct result for diffraction minima.

A. a sinθ = nλ

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. a sinθ = nλ

Detailed solution: The governing wave-optics result is a sinθ = nλ.

M10In CBSE style, select the correct result for central diffraction width.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. 2Dλ/a

Answer: D. 2Dλ/a

Detailed solution: The governing wave-optics result is 2Dλ/a.

M11In CBSE style, select the correct result for Malus law.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. I = Iₚcos²θ

D. frequency always changes

Answer: C. I = Iₚcos²θ

Detailed solution: The governing wave-optics result is I = Iₚcos²θ.

M12In CBSE style, select the correct result for Brewster law.

A. path difference equals phase difference

B. μ = tan iₚ

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. μ = tan iₚ

Detailed solution: The governing wave-optics result is μ = tan iₚ.

M13In CBSE style, select the correct result for wavefront normal.

A. is parallel to ray direction

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. is parallel to ray direction

Detailed solution: The governing wave-optics result is is parallel to ray direction.

M14In CBSE style, select the correct result for Snell law.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. n₁sin i = n₂sin r

Answer: D. n₁sin i = n₂sin r

Detailed solution: The governing wave-optics result is n₁sin i = n₂sin r.

M15In CBSE style, select the correct result for bright interference.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. Δ = nλ

D. frequency always changes

Answer: C. Δ = nλ

Detailed solution: The governing wave-optics result is Δ = nλ.

M16In CBSE style, select the correct result for dark interference.

A. path difference equals phase difference

B. Δ = (2n−1)λ/2

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. Δ = (2n−1)λ/2

Detailed solution: The governing wave-optics result is Δ = (2n−1)λ/2.

M17In CBSE style, select the correct result for phase relation.

A. φ = 2πΔ/λ

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. φ = 2πΔ/λ

Detailed solution: The governing wave-optics result is φ = 2πΔ/λ.

M18In CBSE style, select the correct result for YDSE fringe width.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. β = λD/d

Answer: D. β = λD/d

Detailed solution: The governing wave-optics result is β = λD/d.

M19In CBSE style, select the correct result for thin-sheet shift.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. Δx = D(μ−1)t/d

D. frequency always changes

Answer: C. Δx = D(μ−1)t/d

Detailed solution: The governing wave-optics result is Δx = D(μ−1)t/d.

M20In CBSE style, select the correct result for liquid immersion.

A. path difference equals phase difference

B. β′ = β/μ

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. β′ = β/μ

Detailed solution: The governing wave-optics result is β′ = β/μ.

M21In CBSE style, select the correct result for diffraction minima.

A. a sinθ = nλ

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. a sinθ = nλ

Detailed solution: The governing wave-optics result is a sinθ = nλ.

M22In CBSE style, select the correct result for central diffraction width.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. 2Dλ/a

Answer: D. 2Dλ/a

Detailed solution: The governing wave-optics result is 2Dλ/a.

M23In CBSE style, select the correct result for Malus law.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. I = Iₚcos²θ

D. frequency always changes

Answer: C. I = Iₚcos²θ

Detailed solution: The governing wave-optics result is I = Iₚcos²θ.

M24In CBSE style, select the correct result for Brewster law.

A. path difference equals phase difference

B. μ = tan iₚ

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. μ = tan iₚ

Detailed solution: The governing wave-optics result is μ = tan iₚ.

M25In CBSE style, select the correct result for wavefront normal.

A. is parallel to ray direction

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. is parallel to ray direction

Detailed solution: The governing wave-optics result is is parallel to ray direction.

10 Assertion-Reason

AR1Assertion: wavefront normal follows the standard formula. Reason: is parallel to ray direction.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula is parallel to ray direction directly supports the assertion.

AR2Assertion: Snell law follows the standard formula. Reason: n₁sin i = n₂sin r.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula n₁sin i = n₂sin r directly supports the assertion.

AR3Assertion: bright interference follows the standard formula. Reason: Δ = nλ.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula Δ = nλ directly supports the assertion.

AR4Assertion: dark interference follows the standard formula. Reason: Δ = (2n−1)λ/2.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula Δ = (2n−1)λ/2 directly supports the assertion.

AR5Assertion: phase relation follows the standard formula. Reason: φ = 2πΔ/λ.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula φ = 2πΔ/λ directly supports the assertion.

AR6Assertion: YDSE fringe width follows the standard formula. Reason: β = λD/d.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula β = λD/d directly supports the assertion.

AR7Assertion: thin-sheet shift follows the standard formula. Reason: Δx = D(μ−1)t/d.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula Δx = D(μ−1)t/d directly supports the assertion.

AR8Assertion: liquid immersion follows the standard formula. Reason: β′ = β/μ.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula β′ = β/μ directly supports the assertion.

AR9Assertion: diffraction minima follows the standard formula. Reason: a sinθ = nλ.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula a sinθ = nλ directly supports the assertion.

AR10Assertion: central diffraction width follows the standard formula. Reason: 2Dλ/a.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula 2Dλ/a directly supports the assertion.

15 Numericals

N1For λ = 500 nm, D = 1.5 m and d = 0.5 mm, calculate β.

Answer: 1.500 mm

Detailed solution: Use β = λD/d and convert SI units.

N2A slit of width 0.25 mm uses λ = 505 nm. Find first-minimum angle.

Answer: 2.020e-3 rad

Detailed solution: For small angle, θ₁ = λ/a.

N3A plate of μ = 1.5 and thickness 4 μm is inserted in YDSE with D = 2 m and d = 0.5 mm. Find Δx.

Answer: 8.00 mm

Detailed solution: Use Δx = D(μ−1)t/d.

N4At path difference Δ = 4/4 λ, find φ.

Answer: 2.00π rad

Detailed solution: φ = 2πΔ/λ.

N5Unpolarised intensity is 24 W m⁻². Find intensity after an ideal polariser.

Answer: 12.0 W m⁻²

Detailed solution: An ideal polariser transmits half the unpolarised intensity.

N6For λ = 550 nm, D = 1.5 m and d = 0.5 mm, calculate β.

Answer: 1.650 mm

Detailed solution: Use β = λD/d and convert SI units.

N7A slit of width 0.25 mm uses λ = 530 nm. Find first-minimum angle.

Answer: 2.120e-3 rad

Detailed solution: For small angle, θ₁ = λ/a.

N8A plate of μ = 1.5 and thickness 4 μm is inserted in YDSE with D = 2 m and d = 0.5 mm. Find Δx.

Answer: 8.00 mm

Detailed solution: Use Δx = D(μ−1)t/d.

N9At path difference Δ = 1/4 λ, find φ.

Answer: 0.50π rad

Detailed solution: φ = 2πΔ/λ.

N10Unpolarised intensity is 29 W m⁻². Find intensity after an ideal polariser.

Answer: 14.5 W m⁻²

Detailed solution: An ideal polariser transmits half the unpolarised intensity.

N11For λ = 600 nm, D = 1.5 m and d = 0.5 mm, calculate β.

Answer: 1.800 mm

Detailed solution: Use β = λD/d and convert SI units.

N12A slit of width 0.25 mm uses λ = 555 nm. Find first-minimum angle.

Answer: 2.220e-3 rad

Detailed solution: For small angle, θ₁ = λ/a.

N13A plate of μ = 1.5 and thickness 4 μm is inserted in YDSE with D = 2 m and d = 0.5 mm. Find Δx.

Answer: 8.00 mm

Detailed solution: Use Δx = D(μ−1)t/d.

N14At path difference Δ = 2/4 λ, find φ.

Answer: 1.00π rad

Detailed solution: φ = 2πΔ/λ.

N15Unpolarised intensity is 34 W m⁻². Find intensity after an ideal polariser.

Answer: 17.0 W m⁻²

Detailed solution: An ideal polariser transmits half the unpolarised intensity.

10 Case Studies

CS1CBSE case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 1.

Answer: is parallel to ray direction

Detailed solution: Identify the phenomenon, apply is parallel to ray direction, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS2CBSE case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 2.

Answer: n₁sin i = n₂sin r

Detailed solution: Identify the phenomenon, apply n₁sin i = n₂sin r, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS3CBSE case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 3.

Answer: Δ = nλ

Detailed solution: Identify the phenomenon, apply Δ = nλ, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS4CBSE case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 4.

Answer: Δ = (2n−1)λ/2

Detailed solution: Identify the phenomenon, apply Δ = (2n−1)λ/2, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS5CBSE case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 5.

Answer: φ = 2πΔ/λ

Detailed solution: Identify the phenomenon, apply φ = 2πΔ/λ, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS6CBSE case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 6.

Answer: β = λD/d

Detailed solution: Identify the phenomenon, apply β = λD/d, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS7CBSE case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 7.

Answer: Δx = D(μ−1)t/d

Detailed solution: Identify the phenomenon, apply Δx = D(μ−1)t/d, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS8CBSE case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 8.

Answer: β′ = β/μ

Detailed solution: Identify the phenomenon, apply β′ = β/μ, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS9CBSE case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 9.

Answer: a sinθ = nλ

Detailed solution: Identify the phenomenon, apply a sinθ = nλ, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS10CBSE case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 10.

Answer: 2Dλ/a

Detailed solution: Identify the phenomenon, apply 2Dλ/a, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

NEET Questions

NEET Question Bank · 60 Questions

25 MCQs

M1In NEET style, select the correct result for wavefront normal.

A. is parallel to ray direction

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. is parallel to ray direction

Detailed solution: The governing wave-optics result is is parallel to ray direction.

M2In NEET style, select the correct result for Snell law.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. n₁sin i = n₂sin r

Answer: D. n₁sin i = n₂sin r

Detailed solution: The governing wave-optics result is n₁sin i = n₂sin r.

M3In NEET style, select the correct result for bright interference.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. Δ = nλ

D. frequency always changes

Answer: C. Δ = nλ

Detailed solution: The governing wave-optics result is Δ = nλ.

M4In NEET style, select the correct result for dark interference.

A. path difference equals phase difference

B. Δ = (2n−1)λ/2

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. Δ = (2n−1)λ/2

Detailed solution: The governing wave-optics result is Δ = (2n−1)λ/2.

M5In NEET style, select the correct result for phase relation.

A. φ = 2πΔ/λ

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. φ = 2πΔ/λ

Detailed solution: The governing wave-optics result is φ = 2πΔ/λ.

M6In NEET style, select the correct result for YDSE fringe width.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. β = λD/d

Answer: D. β = λD/d

Detailed solution: The governing wave-optics result is β = λD/d.

M7In NEET style, select the correct result for thin-sheet shift.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. Δx = D(μ−1)t/d

D. frequency always changes

Answer: C. Δx = D(μ−1)t/d

Detailed solution: The governing wave-optics result is Δx = D(μ−1)t/d.

M8In NEET style, select the correct result for liquid immersion.

A. path difference equals phase difference

B. β′ = β/μ

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. β′ = β/μ

Detailed solution: The governing wave-optics result is β′ = β/μ.

M9In NEET style, select the correct result for diffraction minima.

A. a sinθ = nλ

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. a sinθ = nλ

Detailed solution: The governing wave-optics result is a sinθ = nλ.

M10In NEET style, select the correct result for central diffraction width.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. 2Dλ/a

Answer: D. 2Dλ/a

Detailed solution: The governing wave-optics result is 2Dλ/a.

M11In NEET style, select the correct result for Malus law.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. I = Iₚcos²θ

D. frequency always changes

Answer: C. I = Iₚcos²θ

Detailed solution: The governing wave-optics result is I = Iₚcos²θ.

M12In NEET style, select the correct result for Brewster law.

A. path difference equals phase difference

B. μ = tan iₚ

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. μ = tan iₚ

Detailed solution: The governing wave-optics result is μ = tan iₚ.

M13In NEET style, select the correct result for wavefront normal.

A. is parallel to ray direction

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. is parallel to ray direction

Detailed solution: The governing wave-optics result is is parallel to ray direction.

M14In NEET style, select the correct result for Snell law.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. n₁sin i = n₂sin r

Answer: D. n₁sin i = n₂sin r

Detailed solution: The governing wave-optics result is n₁sin i = n₂sin r.

M15In NEET style, select the correct result for bright interference.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. Δ = nλ

D. frequency always changes

Answer: C. Δ = nλ

Detailed solution: The governing wave-optics result is Δ = nλ.

M16In NEET style, select the correct result for dark interference.

A. path difference equals phase difference

B. Δ = (2n−1)λ/2

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. Δ = (2n−1)λ/2

Detailed solution: The governing wave-optics result is Δ = (2n−1)λ/2.

M17In NEET style, select the correct result for phase relation.

A. φ = 2πΔ/λ

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. φ = 2πΔ/λ

Detailed solution: The governing wave-optics result is φ = 2πΔ/λ.

M18In NEET style, select the correct result for YDSE fringe width.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. β = λD/d

Answer: D. β = λD/d

Detailed solution: The governing wave-optics result is β = λD/d.

M19In NEET style, select the correct result for thin-sheet shift.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. Δx = D(μ−1)t/d

D. frequency always changes

Answer: C. Δx = D(μ−1)t/d

Detailed solution: The governing wave-optics result is Δx = D(μ−1)t/d.

M20In NEET style, select the correct result for liquid immersion.

A. path difference equals phase difference

B. β′ = β/μ

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. β′ = β/μ

Detailed solution: The governing wave-optics result is β′ = β/μ.

M21In NEET style, select the correct result for diffraction minima.

A. a sinθ = nλ

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. a sinθ = nλ

Detailed solution: The governing wave-optics result is a sinθ = nλ.

M22In NEET style, select the correct result for central diffraction width.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. 2Dλ/a

Answer: D. 2Dλ/a

Detailed solution: The governing wave-optics result is 2Dλ/a.

M23In NEET style, select the correct result for Malus law.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. I = Iₚcos²θ

D. frequency always changes

Answer: C. I = Iₚcos²θ

Detailed solution: The governing wave-optics result is I = Iₚcos²θ.

M24In NEET style, select the correct result for Brewster law.

A. path difference equals phase difference

B. μ = tan iₚ

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. μ = tan iₚ

Detailed solution: The governing wave-optics result is μ = tan iₚ.

M25In NEET style, select the correct result for wavefront normal.

A. is parallel to ray direction

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. is parallel to ray direction

Detailed solution: The governing wave-optics result is is parallel to ray direction.

10 Assertion-Reason

AR1Assertion: wavefront normal follows the standard formula. Reason: is parallel to ray direction.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula is parallel to ray direction directly supports the assertion.

AR2Assertion: Snell law follows the standard formula. Reason: n₁sin i = n₂sin r.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula n₁sin i = n₂sin r directly supports the assertion.

AR3Assertion: bright interference follows the standard formula. Reason: Δ = nλ.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula Δ = nλ directly supports the assertion.

AR4Assertion: dark interference follows the standard formula. Reason: Δ = (2n−1)λ/2.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula Δ = (2n−1)λ/2 directly supports the assertion.

AR5Assertion: phase relation follows the standard formula. Reason: φ = 2πΔ/λ.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula φ = 2πΔ/λ directly supports the assertion.

AR6Assertion: YDSE fringe width follows the standard formula. Reason: β = λD/d.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula β = λD/d directly supports the assertion.

AR7Assertion: thin-sheet shift follows the standard formula. Reason: Δx = D(μ−1)t/d.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula Δx = D(μ−1)t/d directly supports the assertion.

AR8Assertion: liquid immersion follows the standard formula. Reason: β′ = β/μ.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula β′ = β/μ directly supports the assertion.

AR9Assertion: diffraction minima follows the standard formula. Reason: a sinθ = nλ.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula a sinθ = nλ directly supports the assertion.

AR10Assertion: central diffraction width follows the standard formula. Reason: 2Dλ/a.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula 2Dλ/a directly supports the assertion.

15 Numericals

N1For λ = 500 nm, D = 1.5 m and d = 0.5 mm, calculate β.

Answer: 1.500 mm

Detailed solution: Use β = λD/d and convert SI units.

N2A slit of width 0.25 mm uses λ = 505 nm. Find first-minimum angle.

Answer: 2.020e-3 rad

Detailed solution: For small angle, θ₁ = λ/a.

N3A plate of μ = 1.5 and thickness 4 μm is inserted in YDSE with D = 2 m and d = 0.5 mm. Find Δx.

Answer: 8.00 mm

Detailed solution: Use Δx = D(μ−1)t/d.

N4At path difference Δ = 4/4 λ, find φ.

Answer: 2.00π rad

Detailed solution: φ = 2πΔ/λ.

N5Unpolarised intensity is 24 W m⁻². Find intensity after an ideal polariser.

Answer: 12.0 W m⁻²

Detailed solution: An ideal polariser transmits half the unpolarised intensity.

N6For λ = 550 nm, D = 1.5 m and d = 0.5 mm, calculate β.

Answer: 1.650 mm

Detailed solution: Use β = λD/d and convert SI units.

N7A slit of width 0.25 mm uses λ = 530 nm. Find first-minimum angle.

Answer: 2.120e-3 rad

Detailed solution: For small angle, θ₁ = λ/a.

N8A plate of μ = 1.5 and thickness 4 μm is inserted in YDSE with D = 2 m and d = 0.5 mm. Find Δx.

Answer: 8.00 mm

Detailed solution: Use Δx = D(μ−1)t/d.

N9At path difference Δ = 1/4 λ, find φ.

Answer: 0.50π rad

Detailed solution: φ = 2πΔ/λ.

N10Unpolarised intensity is 29 W m⁻². Find intensity after an ideal polariser.

Answer: 14.5 W m⁻²

Detailed solution: An ideal polariser transmits half the unpolarised intensity.

N11For λ = 600 nm, D = 1.5 m and d = 0.5 mm, calculate β.

Answer: 1.800 mm

Detailed solution: Use β = λD/d and convert SI units.

N12A slit of width 0.25 mm uses λ = 555 nm. Find first-minimum angle.

Answer: 2.220e-3 rad

Detailed solution: For small angle, θ₁ = λ/a.

N13A plate of μ = 1.5 and thickness 4 μm is inserted in YDSE with D = 2 m and d = 0.5 mm. Find Δx.

Answer: 8.00 mm

Detailed solution: Use Δx = D(μ−1)t/d.

N14At path difference Δ = 2/4 λ, find φ.

Answer: 1.00π rad

Detailed solution: φ = 2πΔ/λ.

N15Unpolarised intensity is 34 W m⁻². Find intensity after an ideal polariser.

Answer: 17.0 W m⁻²

Detailed solution: An ideal polariser transmits half the unpolarised intensity.

10 Case Studies

CS1NEET case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 1.

Answer: is parallel to ray direction

Detailed solution: Identify the phenomenon, apply is parallel to ray direction, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS2NEET case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 2.

Answer: n₁sin i = n₂sin r

Detailed solution: Identify the phenomenon, apply n₁sin i = n₂sin r, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS3NEET case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 3.

Answer: Δ = nλ

Detailed solution: Identify the phenomenon, apply Δ = nλ, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS4NEET case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 4.

Answer: Δ = (2n−1)λ/2

Detailed solution: Identify the phenomenon, apply Δ = (2n−1)λ/2, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS5NEET case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 5.

Answer: φ = 2πΔ/λ

Detailed solution: Identify the phenomenon, apply φ = 2πΔ/λ, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS6NEET case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 6.

Answer: β = λD/d

Detailed solution: Identify the phenomenon, apply β = λD/d, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS7NEET case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 7.

Answer: Δx = D(μ−1)t/d

Detailed solution: Identify the phenomenon, apply Δx = D(μ−1)t/d, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS8NEET case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 8.

Answer: β′ = β/μ

Detailed solution: Identify the phenomenon, apply β′ = β/μ, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS9NEET case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 9.

Answer: a sinθ = nλ

Detailed solution: Identify the phenomenon, apply a sinθ = nλ, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS10NEET case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 10.

Answer: 2Dλ/a

Detailed solution: Identify the phenomenon, apply 2Dλ/a, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

JEE Main Questions

JEE Main Question Bank · 60 Questions

25 MCQs

M1In JEE Main style, select the correct result for wavefront normal.

A. is parallel to ray direction

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. is parallel to ray direction

Detailed solution: The governing wave-optics result is is parallel to ray direction.

M2In JEE Main style, select the correct result for Snell law.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. n₁sin i = n₂sin r

Answer: D. n₁sin i = n₂sin r

Detailed solution: The governing wave-optics result is n₁sin i = n₂sin r.

M3In JEE Main style, select the correct result for bright interference.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. Δ = nλ

D. frequency always changes

Answer: C. Δ = nλ

Detailed solution: The governing wave-optics result is Δ = nλ.

M4In JEE Main style, select the correct result for dark interference.

A. path difference equals phase difference

B. Δ = (2n−1)λ/2

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. Δ = (2n−1)λ/2

Detailed solution: The governing wave-optics result is Δ = (2n−1)λ/2.

M5In JEE Main style, select the correct result for phase relation.

A. φ = 2πΔ/λ

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. φ = 2πΔ/λ

Detailed solution: The governing wave-optics result is φ = 2πΔ/λ.

M6In JEE Main style, select the correct result for YDSE fringe width.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. β = λD/d

Answer: D. β = λD/d

Detailed solution: The governing wave-optics result is β = λD/d.

M7In JEE Main style, select the correct result for thin-sheet shift.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. Δx = D(μ−1)t/d

D. frequency always changes

Answer: C. Δx = D(μ−1)t/d

Detailed solution: The governing wave-optics result is Δx = D(μ−1)t/d.

M8In JEE Main style, select the correct result for liquid immersion.

A. path difference equals phase difference

B. β′ = β/μ

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. β′ = β/μ

Detailed solution: The governing wave-optics result is β′ = β/μ.

M9In JEE Main style, select the correct result for diffraction minima.

A. a sinθ = nλ

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. a sinθ = nλ

Detailed solution: The governing wave-optics result is a sinθ = nλ.

M10In JEE Main style, select the correct result for central diffraction width.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. 2Dλ/a

Answer: D. 2Dλ/a

Detailed solution: The governing wave-optics result is 2Dλ/a.

M11In JEE Main style, select the correct result for Malus law.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. I = Iₚcos²θ

D. frequency always changes

Answer: C. I = Iₚcos²θ

Detailed solution: The governing wave-optics result is I = Iₚcos²θ.

M12In JEE Main style, select the correct result for Brewster law.

A. path difference equals phase difference

B. μ = tan iₚ

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. μ = tan iₚ

Detailed solution: The governing wave-optics result is μ = tan iₚ.

M13In JEE Main style, select the correct result for wavefront normal.

A. is parallel to ray direction

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. is parallel to ray direction

Detailed solution: The governing wave-optics result is is parallel to ray direction.

M14In JEE Main style, select the correct result for Snell law.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. n₁sin i = n₂sin r

Answer: D. n₁sin i = n₂sin r

Detailed solution: The governing wave-optics result is n₁sin i = n₂sin r.

M15In JEE Main style, select the correct result for bright interference.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. Δ = nλ

D. frequency always changes

Answer: C. Δ = nλ

Detailed solution: The governing wave-optics result is Δ = nλ.

M16In JEE Main style, select the correct result for dark interference.

A. path difference equals phase difference

B. Δ = (2n−1)λ/2

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. Δ = (2n−1)λ/2

Detailed solution: The governing wave-optics result is Δ = (2n−1)λ/2.

M17In JEE Main style, select the correct result for phase relation.

A. φ = 2πΔ/λ

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. φ = 2πΔ/λ

Detailed solution: The governing wave-optics result is φ = 2πΔ/λ.

M18In JEE Main style, select the correct result for YDSE fringe width.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. β = λD/d

Answer: D. β = λD/d

Detailed solution: The governing wave-optics result is β = λD/d.

M19In JEE Main style, select the correct result for thin-sheet shift.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. Δx = D(μ−1)t/d

D. frequency always changes

Answer: C. Δx = D(μ−1)t/d

Detailed solution: The governing wave-optics result is Δx = D(μ−1)t/d.

M20In JEE Main style, select the correct result for liquid immersion.

A. path difference equals phase difference

B. β′ = β/μ

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. β′ = β/μ

Detailed solution: The governing wave-optics result is β′ = β/μ.

M21In JEE Main style, select the correct result for diffraction minima.

A. a sinθ = nλ

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. a sinθ = nλ

Detailed solution: The governing wave-optics result is a sinθ = nλ.

M22In JEE Main style, select the correct result for central diffraction width.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. 2Dλ/a

Answer: D. 2Dλ/a

Detailed solution: The governing wave-optics result is 2Dλ/a.

M23In JEE Main style, select the correct result for Malus law.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. I = Iₚcos²θ

D. frequency always changes

Answer: C. I = Iₚcos²θ

Detailed solution: The governing wave-optics result is I = Iₚcos²θ.

M24In JEE Main style, select the correct result for Brewster law.

A. path difference equals phase difference

B. μ = tan iₚ

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. μ = tan iₚ

Detailed solution: The governing wave-optics result is μ = tan iₚ.

M25In JEE Main style, select the correct result for wavefront normal.

A. is parallel to ray direction

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. is parallel to ray direction

Detailed solution: The governing wave-optics result is is parallel to ray direction.

10 Assertion-Reason

AR1Assertion: wavefront normal follows the standard formula. Reason: is parallel to ray direction.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula is parallel to ray direction directly supports the assertion.

AR2Assertion: Snell law follows the standard formula. Reason: n₁sin i = n₂sin r.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula n₁sin i = n₂sin r directly supports the assertion.

AR3Assertion: bright interference follows the standard formula. Reason: Δ = nλ.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula Δ = nλ directly supports the assertion.

AR4Assertion: dark interference follows the standard formula. Reason: Δ = (2n−1)λ/2.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula Δ = (2n−1)λ/2 directly supports the assertion.

AR5Assertion: phase relation follows the standard formula. Reason: φ = 2πΔ/λ.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula φ = 2πΔ/λ directly supports the assertion.

AR6Assertion: YDSE fringe width follows the standard formula. Reason: β = λD/d.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula β = λD/d directly supports the assertion.

AR7Assertion: thin-sheet shift follows the standard formula. Reason: Δx = D(μ−1)t/d.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula Δx = D(μ−1)t/d directly supports the assertion.

AR8Assertion: liquid immersion follows the standard formula. Reason: β′ = β/μ.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula β′ = β/μ directly supports the assertion.

AR9Assertion: diffraction minima follows the standard formula. Reason: a sinθ = nλ.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula a sinθ = nλ directly supports the assertion.

AR10Assertion: central diffraction width follows the standard formula. Reason: 2Dλ/a.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula 2Dλ/a directly supports the assertion.

15 Numericals

N1For λ = 500 nm, D = 1.5 m and d = 0.5 mm, calculate β.

Answer: 1.500 mm

Detailed solution: Use β = λD/d and convert SI units.

N2A slit of width 0.25 mm uses λ = 505 nm. Find first-minimum angle.

Answer: 2.020e-3 rad

Detailed solution: For small angle, θ₁ = λ/a.

N3A plate of μ = 1.5 and thickness 4 μm is inserted in YDSE with D = 2 m and d = 0.5 mm. Find Δx.

Answer: 8.00 mm

Detailed solution: Use Δx = D(μ−1)t/d.

N4At path difference Δ = 4/4 λ, find φ.

Answer: 2.00π rad

Detailed solution: φ = 2πΔ/λ.

N5Unpolarised intensity is 24 W m⁻². Find intensity after an ideal polariser.

Answer: 12.0 W m⁻²

Detailed solution: An ideal polariser transmits half the unpolarised intensity.

N6For λ = 550 nm, D = 1.5 m and d = 0.5 mm, calculate β.

Answer: 1.650 mm

Detailed solution: Use β = λD/d and convert SI units.

N7A slit of width 0.25 mm uses λ = 530 nm. Find first-minimum angle.

Answer: 2.120e-3 rad

Detailed solution: For small angle, θ₁ = λ/a.

N8A plate of μ = 1.5 and thickness 4 μm is inserted in YDSE with D = 2 m and d = 0.5 mm. Find Δx.

Answer: 8.00 mm

Detailed solution: Use Δx = D(μ−1)t/d.

N9At path difference Δ = 1/4 λ, find φ.

Answer: 0.50π rad

Detailed solution: φ = 2πΔ/λ.

N10Unpolarised intensity is 29 W m⁻². Find intensity after an ideal polariser.

Answer: 14.5 W m⁻²

Detailed solution: An ideal polariser transmits half the unpolarised intensity.

N11For λ = 600 nm, D = 1.5 m and d = 0.5 mm, calculate β.

Answer: 1.800 mm

Detailed solution: Use β = λD/d and convert SI units.

N12A slit of width 0.25 mm uses λ = 555 nm. Find first-minimum angle.

Answer: 2.220e-3 rad

Detailed solution: For small angle, θ₁ = λ/a.

N13A plate of μ = 1.5 and thickness 4 μm is inserted in YDSE with D = 2 m and d = 0.5 mm. Find Δx.

Answer: 8.00 mm

Detailed solution: Use Δx = D(μ−1)t/d.

N14At path difference Δ = 2/4 λ, find φ.

Answer: 1.00π rad

Detailed solution: φ = 2πΔ/λ.

N15Unpolarised intensity is 34 W m⁻². Find intensity after an ideal polariser.

Answer: 17.0 W m⁻²

Detailed solution: An ideal polariser transmits half the unpolarised intensity.

10 Case Studies

CS1JEE Main case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 1.

Answer: is parallel to ray direction

Detailed solution: Identify the phenomenon, apply is parallel to ray direction, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS2JEE Main case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 2.

Answer: n₁sin i = n₂sin r

Detailed solution: Identify the phenomenon, apply n₁sin i = n₂sin r, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS3JEE Main case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 3.

Answer: Δ = nλ

Detailed solution: Identify the phenomenon, apply Δ = nλ, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS4JEE Main case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 4.

Answer: Δ = (2n−1)λ/2

Detailed solution: Identify the phenomenon, apply Δ = (2n−1)λ/2, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS5JEE Main case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 5.

Answer: φ = 2πΔ/λ

Detailed solution: Identify the phenomenon, apply φ = 2πΔ/λ, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS6JEE Main case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 6.

Answer: β = λD/d

Detailed solution: Identify the phenomenon, apply β = λD/d, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS7JEE Main case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 7.

Answer: Δx = D(μ−1)t/d

Detailed solution: Identify the phenomenon, apply Δx = D(μ−1)t/d, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS8JEE Main case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 8.

Answer: β′ = β/μ

Detailed solution: Identify the phenomenon, apply β′ = β/μ, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS9JEE Main case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 9.

Answer: a sinθ = nλ

Detailed solution: Identify the phenomenon, apply a sinθ = nλ, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS10JEE Main case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 10.

Answer: 2Dλ/a

Detailed solution: Identify the phenomenon, apply 2Dλ/a, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

JEE Advanced Questions

JEE Advanced Question Bank · 60 Questions

25 MCQs

M1In JEE Advanced style, select the correct result for wavefront normal.

A. is parallel to ray direction

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. is parallel to ray direction

Detailed solution: The governing wave-optics result is is parallel to ray direction.

M2In JEE Advanced style, select the correct result for Snell law.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. n₁sin i = n₂sin r

Answer: D. n₁sin i = n₂sin r

Detailed solution: The governing wave-optics result is n₁sin i = n₂sin r.

M3In JEE Advanced style, select the correct result for bright interference.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. Δ = nλ

D. frequency always changes

Answer: C. Δ = nλ

Detailed solution: The governing wave-optics result is Δ = nλ.

M4In JEE Advanced style, select the correct result for dark interference.

A. path difference equals phase difference

B. Δ = (2n−1)λ/2

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. Δ = (2n−1)λ/2

Detailed solution: The governing wave-optics result is Δ = (2n−1)λ/2.

M5In JEE Advanced style, select the correct result for phase relation.

A. φ = 2πΔ/λ

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. φ = 2πΔ/λ

Detailed solution: The governing wave-optics result is φ = 2πΔ/λ.

M6In JEE Advanced style, select the correct result for YDSE fringe width.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. β = λD/d

Answer: D. β = λD/d

Detailed solution: The governing wave-optics result is β = λD/d.

M7In JEE Advanced style, select the correct result for thin-sheet shift.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. Δx = D(μ−1)t/d

D. frequency always changes

Answer: C. Δx = D(μ−1)t/d

Detailed solution: The governing wave-optics result is Δx = D(μ−1)t/d.

M8In JEE Advanced style, select the correct result for liquid immersion.

A. path difference equals phase difference

B. β′ = β/μ

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. β′ = β/μ

Detailed solution: The governing wave-optics result is β′ = β/μ.

M9In JEE Advanced style, select the correct result for diffraction minima.

A. a sinθ = nλ

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. a sinθ = nλ

Detailed solution: The governing wave-optics result is a sinθ = nλ.

M10In JEE Advanced style, select the correct result for central diffraction width.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. 2Dλ/a

Answer: D. 2Dλ/a

Detailed solution: The governing wave-optics result is 2Dλ/a.

M11In JEE Advanced style, select the correct result for Malus law.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. I = Iₚcos²θ

D. frequency always changes

Answer: C. I = Iₚcos²θ

Detailed solution: The governing wave-optics result is I = Iₚcos²θ.

M12In JEE Advanced style, select the correct result for Brewster law.

A. path difference equals phase difference

B. μ = tan iₚ

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. μ = tan iₚ

Detailed solution: The governing wave-optics result is μ = tan iₚ.

M13In JEE Advanced style, select the correct result for wavefront normal.

A. is parallel to ray direction

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. is parallel to ray direction

Detailed solution: The governing wave-optics result is is parallel to ray direction.

M14In JEE Advanced style, select the correct result for Snell law.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. n₁sin i = n₂sin r

Answer: D. n₁sin i = n₂sin r

Detailed solution: The governing wave-optics result is n₁sin i = n₂sin r.

M15In JEE Advanced style, select the correct result for bright interference.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. Δ = nλ

D. frequency always changes

Answer: C. Δ = nλ

Detailed solution: The governing wave-optics result is Δ = nλ.

M16In JEE Advanced style, select the correct result for dark interference.

A. path difference equals phase difference

B. Δ = (2n−1)λ/2

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. Δ = (2n−1)λ/2

Detailed solution: The governing wave-optics result is Δ = (2n−1)λ/2.

M17In JEE Advanced style, select the correct result for phase relation.

A. φ = 2πΔ/λ

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. φ = 2πΔ/λ

Detailed solution: The governing wave-optics result is φ = 2πΔ/λ.

M18In JEE Advanced style, select the correct result for YDSE fringe width.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. β = λD/d

Answer: D. β = λD/d

Detailed solution: The governing wave-optics result is β = λD/d.

M19In JEE Advanced style, select the correct result for thin-sheet shift.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. Δx = D(μ−1)t/d

D. frequency always changes

Answer: C. Δx = D(μ−1)t/d

Detailed solution: The governing wave-optics result is Δx = D(μ−1)t/d.

M20In JEE Advanced style, select the correct result for liquid immersion.

A. path difference equals phase difference

B. β′ = β/μ

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. β′ = β/μ

Detailed solution: The governing wave-optics result is β′ = β/μ.

M21In JEE Advanced style, select the correct result for diffraction minima.

A. a sinθ = nλ

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. a sinθ = nλ

Detailed solution: The governing wave-optics result is a sinθ = nλ.

M22In JEE Advanced style, select the correct result for central diffraction width.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. 2Dλ/a

Answer: D. 2Dλ/a

Detailed solution: The governing wave-optics result is 2Dλ/a.

M23In JEE Advanced style, select the correct result for Malus law.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. I = Iₚcos²θ

D. frequency always changes

Answer: C. I = Iₚcos²θ

Detailed solution: The governing wave-optics result is I = Iₚcos²θ.

M24In JEE Advanced style, select the correct result for Brewster law.

A. path difference equals phase difference

B. μ = tan iₚ

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. μ = tan iₚ

Detailed solution: The governing wave-optics result is μ = tan iₚ.

M25In JEE Advanced style, select the correct result for wavefront normal.

A. is parallel to ray direction

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. is parallel to ray direction

Detailed solution: The governing wave-optics result is is parallel to ray direction.

10 Assertion-Reason

AR1Assertion: wavefront normal follows the standard formula. Reason: is parallel to ray direction.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula is parallel to ray direction directly supports the assertion.

AR2Assertion: Snell law follows the standard formula. Reason: n₁sin i = n₂sin r.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula n₁sin i = n₂sin r directly supports the assertion.

AR3Assertion: bright interference follows the standard formula. Reason: Δ = nλ.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula Δ = nλ directly supports the assertion.

AR4Assertion: dark interference follows the standard formula. Reason: Δ = (2n−1)λ/2.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula Δ = (2n−1)λ/2 directly supports the assertion.

AR5Assertion: phase relation follows the standard formula. Reason: φ = 2πΔ/λ.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula φ = 2πΔ/λ directly supports the assertion.

AR6Assertion: YDSE fringe width follows the standard formula. Reason: β = λD/d.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula β = λD/d directly supports the assertion.

AR7Assertion: thin-sheet shift follows the standard formula. Reason: Δx = D(μ−1)t/d.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula Δx = D(μ−1)t/d directly supports the assertion.

AR8Assertion: liquid immersion follows the standard formula. Reason: β′ = β/μ.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula β′ = β/μ directly supports the assertion.

AR9Assertion: diffraction minima follows the standard formula. Reason: a sinθ = nλ.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula a sinθ = nλ directly supports the assertion.

AR10Assertion: central diffraction width follows the standard formula. Reason: 2Dλ/a.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula 2Dλ/a directly supports the assertion.

15 Numericals

N1For λ = 500 nm, D = 1.5 m and d = 0.5 mm, calculate β.

Answer: 1.500 mm

Detailed solution: Use β = λD/d and convert SI units.

N2A slit of width 0.25 mm uses λ = 505 nm. Find first-minimum angle.

Answer: 2.020e-3 rad

Detailed solution: For small angle, θ₁ = λ/a.

N3A plate of μ = 1.5 and thickness 4 μm is inserted in YDSE with D = 2 m and d = 0.5 mm. Find Δx.

Answer: 8.00 mm

Detailed solution: Use Δx = D(μ−1)t/d.

N4At path difference Δ = 4/4 λ, find φ.

Answer: 2.00π rad

Detailed solution: φ = 2πΔ/λ.

N5Unpolarised intensity is 24 W m⁻². Find intensity after an ideal polariser.

Answer: 12.0 W m⁻²

Detailed solution: An ideal polariser transmits half the unpolarised intensity.

N6For λ = 550 nm, D = 1.5 m and d = 0.5 mm, calculate β.

Answer: 1.650 mm

Detailed solution: Use β = λD/d and convert SI units.

N7A slit of width 0.25 mm uses λ = 530 nm. Find first-minimum angle.

Answer: 2.120e-3 rad

Detailed solution: For small angle, θ₁ = λ/a.

N8A plate of μ = 1.5 and thickness 4 μm is inserted in YDSE with D = 2 m and d = 0.5 mm. Find Δx.

Answer: 8.00 mm

Detailed solution: Use Δx = D(μ−1)t/d.

N9At path difference Δ = 1/4 λ, find φ.

Answer: 0.50π rad

Detailed solution: φ = 2πΔ/λ.

N10Unpolarised intensity is 29 W m⁻². Find intensity after an ideal polariser.

Answer: 14.5 W m⁻²

Detailed solution: An ideal polariser transmits half the unpolarised intensity.

N11For λ = 600 nm, D = 1.5 m and d = 0.5 mm, calculate β.

Answer: 1.800 mm

Detailed solution: Use β = λD/d and convert SI units.

N12A slit of width 0.25 mm uses λ = 555 nm. Find first-minimum angle.

Answer: 2.220e-3 rad

Detailed solution: For small angle, θ₁ = λ/a.

N13A plate of μ = 1.5 and thickness 4 μm is inserted in YDSE with D = 2 m and d = 0.5 mm. Find Δx.

Answer: 8.00 mm

Detailed solution: Use Δx = D(μ−1)t/d.

N14At path difference Δ = 2/4 λ, find φ.

Answer: 1.00π rad

Detailed solution: φ = 2πΔ/λ.

N15Unpolarised intensity is 34 W m⁻². Find intensity after an ideal polariser.

Answer: 17.0 W m⁻²

Detailed solution: An ideal polariser transmits half the unpolarised intensity.

10 Case Studies

CS1JEE Advanced case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 1.

Answer: is parallel to ray direction

Detailed solution: Identify the phenomenon, apply is parallel to ray direction, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS2JEE Advanced case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 2.

Answer: n₁sin i = n₂sin r

Detailed solution: Identify the phenomenon, apply n₁sin i = n₂sin r, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS3JEE Advanced case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 3.

Answer: Δ = nλ

Detailed solution: Identify the phenomenon, apply Δ = nλ, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS4JEE Advanced case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 4.

Answer: Δ = (2n−1)λ/2

Detailed solution: Identify the phenomenon, apply Δ = (2n−1)λ/2, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS5JEE Advanced case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 5.

Answer: φ = 2πΔ/λ

Detailed solution: Identify the phenomenon, apply φ = 2πΔ/λ, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS6JEE Advanced case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 6.

Answer: β = λD/d

Detailed solution: Identify the phenomenon, apply β = λD/d, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS7JEE Advanced case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 7.

Answer: Δx = D(μ−1)t/d

Detailed solution: Identify the phenomenon, apply Δx = D(μ−1)t/d, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS8JEE Advanced case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 8.

Answer: β′ = β/μ

Detailed solution: Identify the phenomenon, apply β′ = β/μ, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS9JEE Advanced case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 9.

Answer: a sinθ = nλ

Detailed solution: Identify the phenomenon, apply a sinθ = nλ, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS10JEE Advanced case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 10.

Answer: 2Dλ/a

Detailed solution: Identify the phenomenon, apply 2Dλ/a, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

IB Physics Questions

IB Physics Question Bank · 60 Questions

25 MCQs

M1In IB Physics style, select the correct result for wavefront normal.

A. is parallel to ray direction

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. is parallel to ray direction

Detailed solution: The governing wave-optics result is is parallel to ray direction.

M2In IB Physics style, select the correct result for Snell law.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. n₁sin i = n₂sin r

Answer: D. n₁sin i = n₂sin r

Detailed solution: The governing wave-optics result is n₁sin i = n₂sin r.

M3In IB Physics style, select the correct result for bright interference.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. Δ = nλ

D. frequency always changes

Answer: C. Δ = nλ

Detailed solution: The governing wave-optics result is Δ = nλ.

M4In IB Physics style, select the correct result for dark interference.

A. path difference equals phase difference

B. Δ = (2n−1)λ/2

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. Δ = (2n−1)λ/2

Detailed solution: The governing wave-optics result is Δ = (2n−1)λ/2.

M5In IB Physics style, select the correct result for phase relation.

A. φ = 2πΔ/λ

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. φ = 2πΔ/λ

Detailed solution: The governing wave-optics result is φ = 2πΔ/λ.

M6In IB Physics style, select the correct result for YDSE fringe width.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. β = λD/d

Answer: D. β = λD/d

Detailed solution: The governing wave-optics result is β = λD/d.

M7In IB Physics style, select the correct result for thin-sheet shift.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. Δx = D(μ−1)t/d

D. frequency always changes

Answer: C. Δx = D(μ−1)t/d

Detailed solution: The governing wave-optics result is Δx = D(μ−1)t/d.

M8In IB Physics style, select the correct result for liquid immersion.

A. path difference equals phase difference

B. β′ = β/μ

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. β′ = β/μ

Detailed solution: The governing wave-optics result is β′ = β/μ.

M9In IB Physics style, select the correct result for diffraction minima.

A. a sinθ = nλ

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. a sinθ = nλ

Detailed solution: The governing wave-optics result is a sinθ = nλ.

M10In IB Physics style, select the correct result for central diffraction width.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. 2Dλ/a

Answer: D. 2Dλ/a

Detailed solution: The governing wave-optics result is 2Dλ/a.

M11In IB Physics style, select the correct result for Malus law.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. I = Iₚcos²θ

D. frequency always changes

Answer: C. I = Iₚcos²θ

Detailed solution: The governing wave-optics result is I = Iₚcos²θ.

M12In IB Physics style, select the correct result for Brewster law.

A. path difference equals phase difference

B. μ = tan iₚ

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. μ = tan iₚ

Detailed solution: The governing wave-optics result is μ = tan iₚ.

M13In IB Physics style, select the correct result for wavefront normal.

A. is parallel to ray direction

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. is parallel to ray direction

Detailed solution: The governing wave-optics result is is parallel to ray direction.

M14In IB Physics style, select the correct result for Snell law.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. n₁sin i = n₂sin r

Answer: D. n₁sin i = n₂sin r

Detailed solution: The governing wave-optics result is n₁sin i = n₂sin r.

M15In IB Physics style, select the correct result for bright interference.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. Δ = nλ

D. frequency always changes

Answer: C. Δ = nλ

Detailed solution: The governing wave-optics result is Δ = nλ.

M16In IB Physics style, select the correct result for dark interference.

A. path difference equals phase difference

B. Δ = (2n−1)λ/2

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. Δ = (2n−1)λ/2

Detailed solution: The governing wave-optics result is Δ = (2n−1)λ/2.

M17In IB Physics style, select the correct result for phase relation.

A. φ = 2πΔ/λ

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. φ = 2πΔ/λ

Detailed solution: The governing wave-optics result is φ = 2πΔ/λ.

M18In IB Physics style, select the correct result for YDSE fringe width.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. β = λD/d

Answer: D. β = λD/d

Detailed solution: The governing wave-optics result is β = λD/d.

M19In IB Physics style, select the correct result for thin-sheet shift.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. Δx = D(μ−1)t/d

D. frequency always changes

Answer: C. Δx = D(μ−1)t/d

Detailed solution: The governing wave-optics result is Δx = D(μ−1)t/d.

M20In IB Physics style, select the correct result for liquid immersion.

A. path difference equals phase difference

B. β′ = β/μ

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. β′ = β/μ

Detailed solution: The governing wave-optics result is β′ = β/μ.

M21In IB Physics style, select the correct result for diffraction minima.

A. a sinθ = nλ

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. a sinθ = nλ

Detailed solution: The governing wave-optics result is a sinθ = nλ.

M22In IB Physics style, select the correct result for central diffraction width.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. 2Dλ/a

Answer: D. 2Dλ/a

Detailed solution: The governing wave-optics result is 2Dλ/a.

M23In IB Physics style, select the correct result for Malus law.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. I = Iₚcos²θ

D. frequency always changes

Answer: C. I = Iₚcos²θ

Detailed solution: The governing wave-optics result is I = Iₚcos²θ.

M24In IB Physics style, select the correct result for Brewster law.

A. path difference equals phase difference

B. μ = tan iₚ

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. μ = tan iₚ

Detailed solution: The governing wave-optics result is μ = tan iₚ.

M25In IB Physics style, select the correct result for wavefront normal.

A. is parallel to ray direction

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. is parallel to ray direction

Detailed solution: The governing wave-optics result is is parallel to ray direction.

10 Assertion-Reason

AR1Assertion: wavefront normal follows the standard formula. Reason: is parallel to ray direction.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula is parallel to ray direction directly supports the assertion.

AR2Assertion: Snell law follows the standard formula. Reason: n₁sin i = n₂sin r.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula n₁sin i = n₂sin r directly supports the assertion.

AR3Assertion: bright interference follows the standard formula. Reason: Δ = nλ.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula Δ = nλ directly supports the assertion.

AR4Assertion: dark interference follows the standard formula. Reason: Δ = (2n−1)λ/2.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula Δ = (2n−1)λ/2 directly supports the assertion.

AR5Assertion: phase relation follows the standard formula. Reason: φ = 2πΔ/λ.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula φ = 2πΔ/λ directly supports the assertion.

AR6Assertion: YDSE fringe width follows the standard formula. Reason: β = λD/d.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula β = λD/d directly supports the assertion.

AR7Assertion: thin-sheet shift follows the standard formula. Reason: Δx = D(μ−1)t/d.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula Δx = D(μ−1)t/d directly supports the assertion.

AR8Assertion: liquid immersion follows the standard formula. Reason: β′ = β/μ.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula β′ = β/μ directly supports the assertion.

AR9Assertion: diffraction minima follows the standard formula. Reason: a sinθ = nλ.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula a sinθ = nλ directly supports the assertion.

AR10Assertion: central diffraction width follows the standard formula. Reason: 2Dλ/a.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula 2Dλ/a directly supports the assertion.

15 Numericals

N1For λ = 500 nm, D = 1.5 m and d = 0.5 mm, calculate β.

Answer: 1.500 mm

Detailed solution: Use β = λD/d and convert SI units.

N2A slit of width 0.25 mm uses λ = 505 nm. Find first-minimum angle.

Answer: 2.020e-3 rad

Detailed solution: For small angle, θ₁ = λ/a.

N3A plate of μ = 1.5 and thickness 4 μm is inserted in YDSE with D = 2 m and d = 0.5 mm. Find Δx.

Answer: 8.00 mm

Detailed solution: Use Δx = D(μ−1)t/d.

N4At path difference Δ = 4/4 λ, find φ.

Answer: 2.00π rad

Detailed solution: φ = 2πΔ/λ.

N5Unpolarised intensity is 24 W m⁻². Find intensity after an ideal polariser.

Answer: 12.0 W m⁻²

Detailed solution: An ideal polariser transmits half the unpolarised intensity.

N6For λ = 550 nm, D = 1.5 m and d = 0.5 mm, calculate β.

Answer: 1.650 mm

Detailed solution: Use β = λD/d and convert SI units.

N7A slit of width 0.25 mm uses λ = 530 nm. Find first-minimum angle.

Answer: 2.120e-3 rad

Detailed solution: For small angle, θ₁ = λ/a.

N8A plate of μ = 1.5 and thickness 4 μm is inserted in YDSE with D = 2 m and d = 0.5 mm. Find Δx.

Answer: 8.00 mm

Detailed solution: Use Δx = D(μ−1)t/d.

N9At path difference Δ = 1/4 λ, find φ.

Answer: 0.50π rad

Detailed solution: φ = 2πΔ/λ.

N10Unpolarised intensity is 29 W m⁻². Find intensity after an ideal polariser.

Answer: 14.5 W m⁻²

Detailed solution: An ideal polariser transmits half the unpolarised intensity.

N11For λ = 600 nm, D = 1.5 m and d = 0.5 mm, calculate β.

Answer: 1.800 mm

Detailed solution: Use β = λD/d and convert SI units.

N12A slit of width 0.25 mm uses λ = 555 nm. Find first-minimum angle.

Answer: 2.220e-3 rad

Detailed solution: For small angle, θ₁ = λ/a.

N13A plate of μ = 1.5 and thickness 4 μm is inserted in YDSE with D = 2 m and d = 0.5 mm. Find Δx.

Answer: 8.00 mm

Detailed solution: Use Δx = D(μ−1)t/d.

N14At path difference Δ = 2/4 λ, find φ.

Answer: 1.00π rad

Detailed solution: φ = 2πΔ/λ.

N15Unpolarised intensity is 34 W m⁻². Find intensity after an ideal polariser.

Answer: 17.0 W m⁻²

Detailed solution: An ideal polariser transmits half the unpolarised intensity.

10 Case Studies

CS1IB Physics case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 1.

Answer: is parallel to ray direction

Detailed solution: Identify the phenomenon, apply is parallel to ray direction, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS2IB Physics case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 2.

Answer: n₁sin i = n₂sin r

Detailed solution: Identify the phenomenon, apply n₁sin i = n₂sin r, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS3IB Physics case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 3.

Answer: Δ = nλ

Detailed solution: Identify the phenomenon, apply Δ = nλ, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS4IB Physics case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 4.

Answer: Δ = (2n−1)λ/2

Detailed solution: Identify the phenomenon, apply Δ = (2n−1)λ/2, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS5IB Physics case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 5.

Answer: φ = 2πΔ/λ

Detailed solution: Identify the phenomenon, apply φ = 2πΔ/λ, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS6IB Physics case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 6.

Answer: β = λD/d

Detailed solution: Identify the phenomenon, apply β = λD/d, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS7IB Physics case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 7.

Answer: Δx = D(μ−1)t/d

Detailed solution: Identify the phenomenon, apply Δx = D(μ−1)t/d, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS8IB Physics case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 8.

Answer: β′ = β/μ

Detailed solution: Identify the phenomenon, apply β′ = β/μ, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS9IB Physics case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 9.

Answer: a sinθ = nλ

Detailed solution: Identify the phenomenon, apply a sinθ = nλ, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS10IB Physics case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 10.

Answer: 2Dλ/a

Detailed solution: Identify the phenomenon, apply 2Dλ/a, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

IGCSE Questions

IGCSE Question Bank · 60 Questions

25 MCQs

M1In IGCSE style, select the correct result for wavefront normal.

A. is parallel to ray direction

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. is parallel to ray direction

Detailed solution: The governing wave-optics result is is parallel to ray direction.

M2In IGCSE style, select the correct result for Snell law.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. n₁sin i = n₂sin r

Answer: D. n₁sin i = n₂sin r

Detailed solution: The governing wave-optics result is n₁sin i = n₂sin r.

M3In IGCSE style, select the correct result for bright interference.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. Δ = nλ

D. frequency always changes

Answer: C. Δ = nλ

Detailed solution: The governing wave-optics result is Δ = nλ.

M4In IGCSE style, select the correct result for dark interference.

A. path difference equals phase difference

B. Δ = (2n−1)λ/2

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. Δ = (2n−1)λ/2

Detailed solution: The governing wave-optics result is Δ = (2n−1)λ/2.

M5In IGCSE style, select the correct result for phase relation.

A. φ = 2πΔ/λ

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. φ = 2πΔ/λ

Detailed solution: The governing wave-optics result is φ = 2πΔ/λ.

M6In IGCSE style, select the correct result for YDSE fringe width.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. β = λD/d

Answer: D. β = λD/d

Detailed solution: The governing wave-optics result is β = λD/d.

M7In IGCSE style, select the correct result for thin-sheet shift.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. Δx = D(μ−1)t/d

D. frequency always changes

Answer: C. Δx = D(μ−1)t/d

Detailed solution: The governing wave-optics result is Δx = D(μ−1)t/d.

M8In IGCSE style, select the correct result for liquid immersion.

A. path difference equals phase difference

B. β′ = β/μ

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. β′ = β/μ

Detailed solution: The governing wave-optics result is β′ = β/μ.

M9In IGCSE style, select the correct result for diffraction minima.

A. a sinθ = nλ

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. a sinθ = nλ

Detailed solution: The governing wave-optics result is a sinθ = nλ.

M10In IGCSE style, select the correct result for central diffraction width.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. 2Dλ/a

Answer: D. 2Dλ/a

Detailed solution: The governing wave-optics result is 2Dλ/a.

M11In IGCSE style, select the correct result for Malus law.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. I = Iₚcos²θ

D. frequency always changes

Answer: C. I = Iₚcos²θ

Detailed solution: The governing wave-optics result is I = Iₚcos²θ.

M12In IGCSE style, select the correct result for Brewster law.

A. path difference equals phase difference

B. μ = tan iₚ

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. μ = tan iₚ

Detailed solution: The governing wave-optics result is μ = tan iₚ.

M13In IGCSE style, select the correct result for wavefront normal.

A. is parallel to ray direction

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. is parallel to ray direction

Detailed solution: The governing wave-optics result is is parallel to ray direction.

M14In IGCSE style, select the correct result for Snell law.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. n₁sin i = n₂sin r

Answer: D. n₁sin i = n₂sin r

Detailed solution: The governing wave-optics result is n₁sin i = n₂sin r.

M15In IGCSE style, select the correct result for bright interference.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. Δ = nλ

D. frequency always changes

Answer: C. Δ = nλ

Detailed solution: The governing wave-optics result is Δ = nλ.

M16In IGCSE style, select the correct result for dark interference.

A. path difference equals phase difference

B. Δ = (2n−1)λ/2

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. Δ = (2n−1)λ/2

Detailed solution: The governing wave-optics result is Δ = (2n−1)λ/2.

M17In IGCSE style, select the correct result for phase relation.

A. φ = 2πΔ/λ

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. φ = 2πΔ/λ

Detailed solution: The governing wave-optics result is φ = 2πΔ/λ.

M18In IGCSE style, select the correct result for YDSE fringe width.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. β = λD/d

Answer: D. β = λD/d

Detailed solution: The governing wave-optics result is β = λD/d.

M19In IGCSE style, select the correct result for thin-sheet shift.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. Δx = D(μ−1)t/d

D. frequency always changes

Answer: C. Δx = D(μ−1)t/d

Detailed solution: The governing wave-optics result is Δx = D(μ−1)t/d.

M20In IGCSE style, select the correct result for liquid immersion.

A. path difference equals phase difference

B. β′ = β/μ

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. β′ = β/μ

Detailed solution: The governing wave-optics result is β′ = β/μ.

M21In IGCSE style, select the correct result for diffraction minima.

A. a sinθ = nλ

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. a sinθ = nλ

Detailed solution: The governing wave-optics result is a sinθ = nλ.

M22In IGCSE style, select the correct result for central diffraction width.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. 2Dλ/a

Answer: D. 2Dλ/a

Detailed solution: The governing wave-optics result is 2Dλ/a.

M23In IGCSE style, select the correct result for Malus law.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. I = Iₚcos²θ

D. frequency always changes

Answer: C. I = Iₚcos²θ

Detailed solution: The governing wave-optics result is I = Iₚcos²θ.

M24In IGCSE style, select the correct result for Brewster law.

A. path difference equals phase difference

B. μ = tan iₚ

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. μ = tan iₚ

Detailed solution: The governing wave-optics result is μ = tan iₚ.

M25In IGCSE style, select the correct result for wavefront normal.

A. is parallel to ray direction

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. is parallel to ray direction

Detailed solution: The governing wave-optics result is is parallel to ray direction.

10 Assertion-Reason

AR1Assertion: wavefront normal follows the standard formula. Reason: is parallel to ray direction.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula is parallel to ray direction directly supports the assertion.

AR2Assertion: Snell law follows the standard formula. Reason: n₁sin i = n₂sin r.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula n₁sin i = n₂sin r directly supports the assertion.

AR3Assertion: bright interference follows the standard formula. Reason: Δ = nλ.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula Δ = nλ directly supports the assertion.

AR4Assertion: dark interference follows the standard formula. Reason: Δ = (2n−1)λ/2.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula Δ = (2n−1)λ/2 directly supports the assertion.

AR5Assertion: phase relation follows the standard formula. Reason: φ = 2πΔ/λ.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula φ = 2πΔ/λ directly supports the assertion.

AR6Assertion: YDSE fringe width follows the standard formula. Reason: β = λD/d.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula β = λD/d directly supports the assertion.

AR7Assertion: thin-sheet shift follows the standard formula. Reason: Δx = D(μ−1)t/d.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula Δx = D(μ−1)t/d directly supports the assertion.

AR8Assertion: liquid immersion follows the standard formula. Reason: β′ = β/μ.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula β′ = β/μ directly supports the assertion.

AR9Assertion: diffraction minima follows the standard formula. Reason: a sinθ = nλ.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula a sinθ = nλ directly supports the assertion.

AR10Assertion: central diffraction width follows the standard formula. Reason: 2Dλ/a.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula 2Dλ/a directly supports the assertion.

15 Numericals

N1For λ = 500 nm, D = 1.5 m and d = 0.5 mm, calculate β.

Answer: 1.500 mm

Detailed solution: Use β = λD/d and convert SI units.

N2A slit of width 0.25 mm uses λ = 505 nm. Find first-minimum angle.

Answer: 2.020e-3 rad

Detailed solution: For small angle, θ₁ = λ/a.

N3A plate of μ = 1.5 and thickness 4 μm is inserted in YDSE with D = 2 m and d = 0.5 mm. Find Δx.

Answer: 8.00 mm

Detailed solution: Use Δx = D(μ−1)t/d.

N4At path difference Δ = 4/4 λ, find φ.

Answer: 2.00π rad

Detailed solution: φ = 2πΔ/λ.

N5Unpolarised intensity is 24 W m⁻². Find intensity after an ideal polariser.

Answer: 12.0 W m⁻²

Detailed solution: An ideal polariser transmits half the unpolarised intensity.

N6For λ = 550 nm, D = 1.5 m and d = 0.5 mm, calculate β.

Answer: 1.650 mm

Detailed solution: Use β = λD/d and convert SI units.

N7A slit of width 0.25 mm uses λ = 530 nm. Find first-minimum angle.

Answer: 2.120e-3 rad

Detailed solution: For small angle, θ₁ = λ/a.

N8A plate of μ = 1.5 and thickness 4 μm is inserted in YDSE with D = 2 m and d = 0.5 mm. Find Δx.

Answer: 8.00 mm

Detailed solution: Use Δx = D(μ−1)t/d.

N9At path difference Δ = 1/4 λ, find φ.

Answer: 0.50π rad

Detailed solution: φ = 2πΔ/λ.

N10Unpolarised intensity is 29 W m⁻². Find intensity after an ideal polariser.

Answer: 14.5 W m⁻²

Detailed solution: An ideal polariser transmits half the unpolarised intensity.

N11For λ = 600 nm, D = 1.5 m and d = 0.5 mm, calculate β.

Answer: 1.800 mm

Detailed solution: Use β = λD/d and convert SI units.

N12A slit of width 0.25 mm uses λ = 555 nm. Find first-minimum angle.

Answer: 2.220e-3 rad

Detailed solution: For small angle, θ₁ = λ/a.

N13A plate of μ = 1.5 and thickness 4 μm is inserted in YDSE with D = 2 m and d = 0.5 mm. Find Δx.

Answer: 8.00 mm

Detailed solution: Use Δx = D(μ−1)t/d.

N14At path difference Δ = 2/4 λ, find φ.

Answer: 1.00π rad

Detailed solution: φ = 2πΔ/λ.

N15Unpolarised intensity is 34 W m⁻². Find intensity after an ideal polariser.

Answer: 17.0 W m⁻²

Detailed solution: An ideal polariser transmits half the unpolarised intensity.

10 Case Studies

CS1IGCSE case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 1.

Answer: is parallel to ray direction

Detailed solution: Identify the phenomenon, apply is parallel to ray direction, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS2IGCSE case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 2.

Answer: n₁sin i = n₂sin r

Detailed solution: Identify the phenomenon, apply n₁sin i = n₂sin r, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS3IGCSE case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 3.

Answer: Δ = nλ

Detailed solution: Identify the phenomenon, apply Δ = nλ, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS4IGCSE case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 4.

Answer: Δ = (2n−1)λ/2

Detailed solution: Identify the phenomenon, apply Δ = (2n−1)λ/2, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS5IGCSE case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 5.

Answer: φ = 2πΔ/λ

Detailed solution: Identify the phenomenon, apply φ = 2πΔ/λ, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS6IGCSE case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 6.

Answer: β = λD/d

Detailed solution: Identify the phenomenon, apply β = λD/d, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS7IGCSE case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 7.

Answer: Δx = D(μ−1)t/d

Detailed solution: Identify the phenomenon, apply Δx = D(μ−1)t/d, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS8IGCSE case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 8.

Answer: β′ = β/μ

Detailed solution: Identify the phenomenon, apply β′ = β/μ, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS9IGCSE case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 9.

Answer: a sinθ = nλ

Detailed solution: Identify the phenomenon, apply a sinθ = nλ, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS10IGCSE case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 10.

Answer: 2Dλ/a

Detailed solution: Identify the phenomenon, apply 2Dλ/a, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

A-Level Questions

A-Level Question Bank · 60 Questions

25 MCQs

M1In A-Level style, select the correct result for wavefront normal.

A. is parallel to ray direction

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. is parallel to ray direction

Detailed solution: The governing wave-optics result is is parallel to ray direction.

M2In A-Level style, select the correct result for Snell law.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. n₁sin i = n₂sin r

Answer: D. n₁sin i = n₂sin r

Detailed solution: The governing wave-optics result is n₁sin i = n₂sin r.

M3In A-Level style, select the correct result for bright interference.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. Δ = nλ

D. frequency always changes

Answer: C. Δ = nλ

Detailed solution: The governing wave-optics result is Δ = nλ.

M4In A-Level style, select the correct result for dark interference.

A. path difference equals phase difference

B. Δ = (2n−1)λ/2

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. Δ = (2n−1)λ/2

Detailed solution: The governing wave-optics result is Δ = (2n−1)λ/2.

M5In A-Level style, select the correct result for phase relation.

A. φ = 2πΔ/λ

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. φ = 2πΔ/λ

Detailed solution: The governing wave-optics result is φ = 2πΔ/λ.

M6In A-Level style, select the correct result for YDSE fringe width.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. β = λD/d

Answer: D. β = λD/d

Detailed solution: The governing wave-optics result is β = λD/d.

M7In A-Level style, select the correct result for thin-sheet shift.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. Δx = D(μ−1)t/d

D. frequency always changes

Answer: C. Δx = D(μ−1)t/d

Detailed solution: The governing wave-optics result is Δx = D(μ−1)t/d.

M8In A-Level style, select the correct result for liquid immersion.

A. path difference equals phase difference

B. β′ = β/μ

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. β′ = β/μ

Detailed solution: The governing wave-optics result is β′ = β/μ.

M9In A-Level style, select the correct result for diffraction minima.

A. a sinθ = nλ

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. a sinθ = nλ

Detailed solution: The governing wave-optics result is a sinθ = nλ.

M10In A-Level style, select the correct result for central diffraction width.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. 2Dλ/a

Answer: D. 2Dλ/a

Detailed solution: The governing wave-optics result is 2Dλ/a.

M11In A-Level style, select the correct result for Malus law.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. I = Iₚcos²θ

D. frequency always changes

Answer: C. I = Iₚcos²θ

Detailed solution: The governing wave-optics result is I = Iₚcos²θ.

M12In A-Level style, select the correct result for Brewster law.

A. path difference equals phase difference

B. μ = tan iₚ

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. μ = tan iₚ

Detailed solution: The governing wave-optics result is μ = tan iₚ.

M13In A-Level style, select the correct result for wavefront normal.

A. is parallel to ray direction

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. is parallel to ray direction

Detailed solution: The governing wave-optics result is is parallel to ray direction.

M14In A-Level style, select the correct result for Snell law.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. n₁sin i = n₂sin r

Answer: D. n₁sin i = n₂sin r

Detailed solution: The governing wave-optics result is n₁sin i = n₂sin r.

M15In A-Level style, select the correct result for bright interference.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. Δ = nλ

D. frequency always changes

Answer: C. Δ = nλ

Detailed solution: The governing wave-optics result is Δ = nλ.

M16In A-Level style, select the correct result for dark interference.

A. path difference equals phase difference

B. Δ = (2n−1)λ/2

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. Δ = (2n−1)λ/2

Detailed solution: The governing wave-optics result is Δ = (2n−1)λ/2.

M17In A-Level style, select the correct result for phase relation.

A. φ = 2πΔ/λ

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. φ = 2πΔ/λ

Detailed solution: The governing wave-optics result is φ = 2πΔ/λ.

M18In A-Level style, select the correct result for YDSE fringe width.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. β = λD/d

Answer: D. β = λD/d

Detailed solution: The governing wave-optics result is β = λD/d.

M19In A-Level style, select the correct result for thin-sheet shift.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. Δx = D(μ−1)t/d

D. frequency always changes

Answer: C. Δx = D(μ−1)t/d

Detailed solution: The governing wave-optics result is Δx = D(μ−1)t/d.

M20In A-Level style, select the correct result for liquid immersion.

A. path difference equals phase difference

B. β′ = β/μ

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. β′ = β/μ

Detailed solution: The governing wave-optics result is β′ = β/μ.

M21In A-Level style, select the correct result for diffraction minima.

A. a sinθ = nλ

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. a sinθ = nλ

Detailed solution: The governing wave-optics result is a sinθ = nλ.

M22In A-Level style, select the correct result for central diffraction width.

A. frequency always changes

B. intensity is proportional to amplitude

C. path difference equals phase difference

D. 2Dλ/a

Answer: D. 2Dλ/a

Detailed solution: The governing wave-optics result is 2Dλ/a.

M23In A-Level style, select the correct result for Malus law.

A. intensity is proportional to amplitude

B. path difference equals phase difference

C. I = Iₚcos²θ

D. frequency always changes

Answer: C. I = Iₚcos²θ

Detailed solution: The governing wave-optics result is I = Iₚcos²θ.

M24In A-Level style, select the correct result for Brewster law.

A. path difference equals phase difference

B. μ = tan iₚ

C. frequency always changes

D. intensity is proportional to amplitude

Answer: B. μ = tan iₚ

Detailed solution: The governing wave-optics result is μ = tan iₚ.

M25In A-Level style, select the correct result for wavefront normal.

A. is parallel to ray direction

B. frequency always changes

C. intensity is proportional to amplitude

D. path difference equals phase difference

Answer: A. is parallel to ray direction

Detailed solution: The governing wave-optics result is is parallel to ray direction.

10 Assertion-Reason

AR1Assertion: wavefront normal follows the standard formula. Reason: is parallel to ray direction.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula is parallel to ray direction directly supports the assertion.

AR2Assertion: Snell law follows the standard formula. Reason: n₁sin i = n₂sin r.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula n₁sin i = n₂sin r directly supports the assertion.

AR3Assertion: bright interference follows the standard formula. Reason: Δ = nλ.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula Δ = nλ directly supports the assertion.

AR4Assertion: dark interference follows the standard formula. Reason: Δ = (2n−1)λ/2.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula Δ = (2n−1)λ/2 directly supports the assertion.

AR5Assertion: phase relation follows the standard formula. Reason: φ = 2πΔ/λ.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula φ = 2πΔ/λ directly supports the assertion.

AR6Assertion: YDSE fringe width follows the standard formula. Reason: β = λD/d.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula β = λD/d directly supports the assertion.

AR7Assertion: thin-sheet shift follows the standard formula. Reason: Δx = D(μ−1)t/d.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula Δx = D(μ−1)t/d directly supports the assertion.

AR8Assertion: liquid immersion follows the standard formula. Reason: β′ = β/μ.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula β′ = β/μ directly supports the assertion.

AR9Assertion: diffraction minima follows the standard formula. Reason: a sinθ = nλ.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula a sinθ = nλ directly supports the assertion.

AR10Assertion: central diffraction width follows the standard formula. Reason: 2Dλ/a.

A. Both true and reason explains assertion

B. Both true but reason does not explain

C. Assertion true, reason false

D. Assertion false, reason true

Answer: A

Detailed solution: The formula 2Dλ/a directly supports the assertion.

15 Numericals

N1For λ = 500 nm, D = 1.5 m and d = 0.5 mm, calculate β.

Answer: 1.500 mm

Detailed solution: Use β = λD/d and convert SI units.

N2A slit of width 0.25 mm uses λ = 505 nm. Find first-minimum angle.

Answer: 2.020e-3 rad

Detailed solution: For small angle, θ₁ = λ/a.

N3A plate of μ = 1.5 and thickness 4 μm is inserted in YDSE with D = 2 m and d = 0.5 mm. Find Δx.

Answer: 8.00 mm

Detailed solution: Use Δx = D(μ−1)t/d.

N4At path difference Δ = 4/4 λ, find φ.

Answer: 2.00π rad

Detailed solution: φ = 2πΔ/λ.

N5Unpolarised intensity is 24 W m⁻². Find intensity after an ideal polariser.

Answer: 12.0 W m⁻²

Detailed solution: An ideal polariser transmits half the unpolarised intensity.

N6For λ = 550 nm, D = 1.5 m and d = 0.5 mm, calculate β.

Answer: 1.650 mm

Detailed solution: Use β = λD/d and convert SI units.

N7A slit of width 0.25 mm uses λ = 530 nm. Find first-minimum angle.

Answer: 2.120e-3 rad

Detailed solution: For small angle, θ₁ = λ/a.

N8A plate of μ = 1.5 and thickness 4 μm is inserted in YDSE with D = 2 m and d = 0.5 mm. Find Δx.

Answer: 8.00 mm

Detailed solution: Use Δx = D(μ−1)t/d.

N9At path difference Δ = 1/4 λ, find φ.

Answer: 0.50π rad

Detailed solution: φ = 2πΔ/λ.

N10Unpolarised intensity is 29 W m⁻². Find intensity after an ideal polariser.

Answer: 14.5 W m⁻²

Detailed solution: An ideal polariser transmits half the unpolarised intensity.

N11For λ = 600 nm, D = 1.5 m and d = 0.5 mm, calculate β.

Answer: 1.800 mm

Detailed solution: Use β = λD/d and convert SI units.

N12A slit of width 0.25 mm uses λ = 555 nm. Find first-minimum angle.

Answer: 2.220e-3 rad

Detailed solution: For small angle, θ₁ = λ/a.

N13A plate of μ = 1.5 and thickness 4 μm is inserted in YDSE with D = 2 m and d = 0.5 mm. Find Δx.

Answer: 8.00 mm

Detailed solution: Use Δx = D(μ−1)t/d.

N14At path difference Δ = 2/4 λ, find φ.

Answer: 1.00π rad

Detailed solution: φ = 2πΔ/λ.

N15Unpolarised intensity is 34 W m⁻². Find intensity after an ideal polariser.

Answer: 17.0 W m⁻²

Detailed solution: An ideal polariser transmits half the unpolarised intensity.

10 Case Studies

CS1A-Level case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 1.

Answer: is parallel to ray direction

Detailed solution: Identify the phenomenon, apply is parallel to ray direction, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS2A-Level case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 2.

Answer: n₁sin i = n₂sin r

Detailed solution: Identify the phenomenon, apply n₁sin i = n₂sin r, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS3A-Level case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 3.

Answer: Δ = nλ

Detailed solution: Identify the phenomenon, apply Δ = nλ, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS4A-Level case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 4.

Answer: Δ = (2n−1)λ/2

Detailed solution: Identify the phenomenon, apply Δ = (2n−1)λ/2, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS5A-Level case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 5.

Answer: φ = 2πΔ/λ

Detailed solution: Identify the phenomenon, apply φ = 2πΔ/λ, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS6A-Level case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 6.

Answer: β = λD/d

Detailed solution: Identify the phenomenon, apply β = λD/d, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS7A-Level case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 7.

Answer: Δx = D(μ−1)t/d

Detailed solution: Identify the phenomenon, apply Δx = D(μ−1)t/d, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS8A-Level case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 8.

Answer: β′ = β/μ

Detailed solution: Identify the phenomenon, apply β′ = β/μ, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS9A-Level case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 9.

Answer: a sinθ = nλ

Detailed solution: Identify the phenomenon, apply a sinθ = nλ, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

CS10A-Level case study: A laboratory changes one parameter in a wave-optics setup. Determine the governing relation and predict the observation for case 10.

Answer: 2Dλ/a

Detailed solution: Identify the phenomenon, apply 2Dλ/a, and hold the remaining parameters constant. The observed pattern follows the proportionality in that relation.

Assertion Reason Questions

Each examination section contains 10 fully explained assertion-reason questions.

CBSE Assertion-Reason NEET Assertion-Reason JEE Main Assertion-Reason JEE Advanced Assertion-Reason IB Physics Assertion-Reason IGCSE Assertion-Reason A-Level Assertion-Reason

Case Study Questions

Each examination section contains 10 solved case-study questions.

CBSE Case Studies NEET Case Studies JEE Main Case Studies JEE Advanced Case Studies IB Physics Case Studies IGCSE Case Studies A-Level Case Studies

Two-Page Revision Notes

Revision Page 1 · Core Ideas

Wavefront

Surface of constant phaseNormals give ray directionHuygens envelope advances the wave

Interference

Δ = nλ → brightΔ = (2n−1)λ/2 → darkI = I₁+I₂+2√(I₁I₂)cosφ

YDSE

β = λD/dThin sheet shifts pattern, not βLiquid reduces β by μ

Diffraction

a sinθ = nλ minimaCentral width = 2Dλ/aCentral band is brightest and widest

Polarisation

I = Iₚcos²θμ = tan iₚShows transverse nature

Common Mistakes

Use Δ for path differenceUse φ for phase differenceUse Δx only for fringe displacement

Revision Page 2 · Exam Attack Plan

Write SI conversions before substituting numerical values.
Identify whether the question asks path difference, phase difference, position or fringe width.
For YDSE coincidence, equate integral multiples of wavelengths.
For diffraction, remember the central width is between the two first minima.
For unpolarised light, apply the one-half factor before Malus law.
Use the exact secondary-maximum equation tanα = α when higher accuracy is requested.
Check whether refractive index changes wavelength, speed or both; frequency stays fixed at an interface.

Most Important NEET

β = λD/da sinθ = nλI = Iₚcos²θ

Most Important JEE

Δx = D(μ−1)t/dMissing order n = m(d/a)tanα = α

Most Important NCERT

Frequency unchanged on refractionCentral diffraction maximum widestRayleigh criterion sets resolution