Amplitude
The electric-field amplitudes add with phase. They may reinforce or oppose one another.
Wave Optics · Chapter 02
Interference of Light
Master superposition, coherent sources, path and phase difference, intensity distribution and Young's Double Slit Experiment for board and competitive examinations.
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01
Principle of Superposition
When two or more light waves overlap in a linear medium, the instantaneous resultant displacement equals the algebraic sum of their individual displacements. The waves continue through one another; interference changes the observed intensity distribution, not the identity of the component waves.
Intensity
Brightness is proportional to the square of resultant amplitude. Therefore I₁/I₂ = a²/b².
Energy
Interference redistributes energy between bright and dark regions; total energy remains conserved.
02
Coherent Sources
Coherent sources emit waves of the same frequency with a constant phase difference.
- Independent lamps are not mutually coherent because their phases fluctuate randomly.
- YDSE produces S₁ and S₂ by dividing one incident wavefront.
- Stable frequency and phase relation create stationary, observable fringes.
Important Conceptual Questions
Q1What is the principle of superposition?
Answer: The resultant displacement is the algebraic sum of individual displacements.
Explanation: Linear waves overlap without permanently changing one another; their instantaneous displacements add.
Q2What are coherent sources?
Answer: Sources with the same frequency and a constant phase difference.
Explanation: Stable interference requires the relative phase to remain fixed with time.
Q3Why do two independent lamps not produce sustained fringes?
Answer: Their phase difference changes randomly.
Explanation: Random atomic emissions make maxima and minima move too rapidly to observe.
Q4What is constructive interference?
Answer: Superposition with phase difference 2nπ.
Explanation: The waves arrive in phase, amplitudes reinforce, and intensity is maximum.
Q5What is destructive interference?
Answer: Superposition with phase difference (2n−1)π.
Explanation: The waves arrive in opposite phase and amplitudes subtract.
Q6How are phase and path difference related?
Answer: φ = 2πΔx/λ.
Explanation: One wavelength of extra path corresponds to a phase change of 2π.
Q7What does phase lead mean?
Answer: One wave reaches a given phase earlier than the other.
Explanation: A positive phase offset indicates advancement relative to the reference wave.
Q8What does phase lag mean?
Answer: One wave reaches a given phase later than the other.
Explanation: A negative relative phase or delayed oscillation indicates lag.
Q9Why is brightness proportional to amplitude squared?
Answer: Wave energy flux is proportional to the square of field amplitude.
Explanation: For light, time-averaged intensity follows the squared electric-field amplitude.
Q10Can unequal amplitudes give zero minimum intensity?
Answer: No.
Explanation: Imin = (a−b)², which vanishes only when a = b.
Q11What is the bright-fringe path condition?
Answer: Δx = nλ.
Explanation: It gives φ = 2nπ and cosφ = 1.
Q12What is the dark-fringe path condition?
Answer: Δx = (2n−1)λ/2.
Explanation: It gives an odd multiple of π phase difference.
Q13Does interference create energy?
Answer: No.
Explanation: Energy is redistributed from dark regions to bright regions; total energy is conserved.
Q14What is fringe visibility?
Answer: V = (Imax−Imin)/(Imax+Imin).
Explanation: It measures contrast and is highest for equal beam intensities.
Q15Why should slits be narrow in YDSE?
Answer: Each slit must act approximately as a coherent secondary source.
Explanation: Narrow slits diffract light broadly so the two beams overlap on the screen.
Q16Why must S₁ and S₂ come from one source?
Answer: Division of one wavefront fixes their relative phase.
Explanation: Illuminating both slits from a common source creates mutual coherence.
Q17What is the central fringe in symmetric YDSE?
Answer: Bright.
Explanation: At the screen center, paths from S₁ and S₂ are equal, so Δx = 0.
Q18What happens if one slit is closed?
Answer: Interference fringes disappear.
Explanation: Only one wave remains, so there is no two-wave cross term.
Q19Does phase difference depend on wavelength?
Answer: Yes for a fixed path difference.
Explanation: φ = 2πΔx/λ, so shorter wavelength gives larger phase difference.
Q20What determines the resultant amplitude?
Answer: a, b and cosφ.
Explanation: R² = a²+b²+2ab cosφ.
03
Constructive and Destructive Interference
Constructive Interference
Destructive Interference
Contrast ratio: Imax/Imin = (a+b)²/(a−b)². If a = b, then Imax = 4a² and Imin = 0.
04
Interference Intensity Derivation
Complete Interference Intensity Derivation
Let y₁ = a sinωt and y₂ = b sin(ωt + φ).
By superposition: y = y₁ + y₂.
y = a sinωt + b sin(ωt + φ).
y = a sinωt + b sinωt cosφ + b cosωt sinφ.
y = (a + b cosφ) sinωt + (b sinφ) cosωt.
Let R cosθ = a + b cosφ and R sinθ = b sinφ.
Squaring and adding: R² = a² + b² + 2ab cosφ.
Since intensity is proportional to amplitude squared: I = a² + b² + 2ab cosφ.
If I₁ ∝ a² and I₂ ∝ b²: I = I₁ + I₂ + 2√(I₁I₂) cosφ.
Equal Intensities
If a = b and each beam has intensity I₀:
I = 2I₀(1+cosφ) = 4I₀cos²(φ/2)In amplitude units: I = 4a²cos²(φ/2).
Maximum, Minimum and Visibility
Imax = (a+b)²
Imin = (a−b)²
V = (Imax−Imin)/(Imax+Imin) = 2ab/(a²+b²)
05
Path Difference and Phase Difference
Path Difference
Phase Lead and Phase Lag
φ = (2π/λ)Δx | Δx = φλ/(2π)
A wave leads if it reaches the same phase earlier; it lags if it reaches that phase later. The sign depends on the chosen reference wave.
06
Interference of Two Coherent Light Beams
The overlapping circular wavefronts from S₁ and S₂ reach the screen with different path differences. At O and P₂-type points the waves reinforce; at P₁-type points they oppose, giving alternating bright and dark fringes.
07
Young's Double Slit Experiment
Geometry
S₁ and S₂ are separated by d. The screen is at distance D, with D ≫ d.
Central Fringe
At the screen center, Δx = 0, so the waves arrive in phase and form the central bright fringe.
Fringe Width
Successive bright or dark fringes are separated by β = λD/d.
08
Applications of Interference
Thin-film colors
Colors arise because reflected beams acquire wavelength-dependent phase differences.
Anti-reflection coatings
A coating creates destructive interference between reflected beams.
Interferometers
Split beams recombine to reveal tiny optical path changes.
Precision wavelength measurement
Known fringe shifts allow accurate wavelength determination.
Refractive-index measurement
Introducing a sample changes optical path and shifts fringes.
Surface testing
Fringe distortion reveals very small surface irregularities.
09
30 Solved Numericals
NEET
1. Maximum intensity
Two waves have amplitudes 2 and 3. Find Imax in proportional units.
Answer: 25
Detailed solution: Imax = (a+b)² = (2+3)² = 25.
NEET
2. Maximum intensity
Two waves have amplitudes 3 and 5. Find Imax in proportional units.
Answer: 64
Detailed solution: Imax = (a+b)² = (3+5)² = 64.
NEET
3. Maximum intensity
Two waves have amplitudes 4 and 1. Find Imax in proportional units.
Answer: 25
Detailed solution: Imax = (a+b)² = (4+1)² = 25.
NEET
4. Maximum intensity
Two waves have amplitudes 5 and 2. Find Imax in proportional units.
Answer: 49
Detailed solution: Imax = (a+b)² = (5+2)² = 49.
NEET
5. Maximum intensity
Two waves have amplitudes 6 and 4. Find Imax in proportional units.
Answer: 100
Detailed solution: Imax = (a+b)² = (6+4)² = 100.
NEET
6. Minimum intensity
Two waves have amplitudes 5 and 2. Find Imin.
Answer: 9
Detailed solution: Imin = (a−b)² = (5−2)² = 9.
NEET
7. Minimum intensity
Two waves have amplitudes 7 and 3. Find Imin.
Answer: 16
Detailed solution: Imin = (a−b)² = (7−3)² = 16.
NEET
8. Minimum intensity
Two waves have amplitudes 8 and 5. Find Imin.
Answer: 9
Detailed solution: Imin = (a−b)² = (8−5)² = 9.
NEET
9. Minimum intensity
Two waves have amplitudes 6 and 1. Find Imin.
Answer: 25
Detailed solution: Imin = (a−b)² = (6−1)² = 25.
NEET
10. Minimum intensity
Two waves have amplitudes 9 and 4. Find Imin.
Answer: 25
Detailed solution: Imin = (a−b)² = (9−4)² = 25.
JEE Main
11. Intensity at phase
Equal beams each have intensity 4. Find resultant intensity at φ = 0°.
Answer: 16.00
Detailed solution: I = 2I₀(1+cosφ) = 8(1+cos0°) = 16.00.
JEE Main
12. Intensity at phase
Equal beams each have intensity 4. Find resultant intensity at φ = 60°.
Answer: 12.00
Detailed solution: I = 2I₀(1+cosφ) = 8(1+cos60°) = 12.00.
JEE Main
13. Intensity at phase
Equal beams each have intensity 5. Find resultant intensity at φ = 90°.
Answer: 10.00
Detailed solution: I = 2I₀(1+cosφ) = 10(1+cos90°) = 10.00.
JEE Main
14. Intensity at phase
Equal beams each have intensity 3. Find resultant intensity at φ = 120°.
Answer: 3.00
Detailed solution: I = 2I₀(1+cosφ) = 6(1+cos120°) = 3.00.
JEE Main
15. Intensity at phase
Equal beams each have intensity 6. Find resultant intensity at φ = 180°.
Answer: 0.00
Detailed solution: I = 2I₀(1+cosφ) = 12(1+cos180°) = 0.00.
JEE Main
16. Path to phase
For path difference 0.25λ, find phase difference.
Answer: 0.50π rad
Detailed solution: φ = 2πΔx/λ = 2π(0.25) = 0.50π rad.
JEE Main
17. Path to phase
For path difference 0.5λ, find phase difference.
Answer: 1.00π rad
Detailed solution: φ = 2πΔx/λ = 2π(0.5) = 1.00π rad.
JEE Main
18. Path to phase
For path difference 0.75λ, find phase difference.
Answer: 1.50π rad
Detailed solution: φ = 2πΔx/λ = 2π(0.75) = 1.50π rad.
JEE Main
19. Path to phase
For path difference 1.5λ, find phase difference.
Answer: 3.00π rad
Detailed solution: φ = 2πΔx/λ = 2π(1.5) = 3.00π rad.
JEE Main
20. Path to phase
For path difference 2.25λ, find phase difference.
Answer: 4.50π rad
Detailed solution: φ = 2πΔx/λ = 2π(2.25) = 4.50π rad.
JEE Main
21. Phase to path
For phase difference 0.5π rad, find path difference.
Answer: 0.25λ
Detailed solution: Δx = φλ/(2π) = 0.5πλ/(2π) = 0.25λ.
JEE Main
22. Phase to path
For phase difference 1π rad, find path difference.
Answer: 0.50λ
Detailed solution: Δx = φλ/(2π) = 1πλ/(2π) = 0.50λ.
JEE Advanced
23. Phase to path
For phase difference 1.5π rad, find path difference.
Answer: 0.75λ
Detailed solution: Δx = φλ/(2π) = 1.5πλ/(2π) = 0.75λ.
JEE Advanced
24. Phase to path
For phase difference 0.25π rad, find path difference.
Answer: 0.13λ
Detailed solution: Δx = φλ/(2π) = 0.25πλ/(2π) = 0.13λ.
JEE Advanced
25. Phase to path
For phase difference 1.75π rad, find path difference.
Answer: 0.88λ
Detailed solution: Δx = φλ/(2π) = 1.75πλ/(2π) = 0.88λ.
JEE Advanced
26. Visibility
The interfering intensities are 9 and 4. Find visibility.
Answer: 0.923
Detailed solution: V = 2√(I₁I₂)/(I₁+I₂) = 0.923.
JEE Advanced
27. Visibility
The interfering intensities are 16 and 4. Find visibility.
Answer: 0.800
Detailed solution: V = 2√(I₁I₂)/(I₁+I₂) = 0.800.
JEE Advanced
28. Visibility
The interfering intensities are 25 and 9. Find visibility.
Answer: 0.882
Detailed solution: V = 2√(I₁I₂)/(I₁+I₂) = 0.882.
JEE Advanced
29. Visibility
The interfering intensities are 10 and 2.5. Find visibility.
Answer: 0.800
Detailed solution: V = 2√(I₁I₂)/(I₁+I₂) = 0.800.
JEE Advanced
30. Visibility
The interfering intensities are 12 and 3. Find visibility.
Answer: 0.800
Detailed solution: V = 2√(I₁I₂)/(I₁+I₂) = 0.800.
10
20 Assertion-Reason Questions
AR1Assertion: Coherent sources have a constant phase difference. Reason: They must have the same frequency.
Answer: A
Explanation: Both are true and equal frequency is necessary for a fixed phase relation.
AR2Assertion: Two independent bulbs normally produce stable interference. Reason: Their emissions have random phase changes.
Answer: D
Explanation: The assertion is false; the reason explains why stable fringes are absent.
AR3Assertion: At constructive interference, intensity is maximum. Reason: The phase difference is 2nπ.
Answer: A
Explanation: Both are true and the phase condition gives cosφ = 1.
AR4Assertion: At destructive interference, energy is destroyed. Reason: Intensity can become zero at some points.
Answer: D
Explanation: The assertion is false; energy is redistributed even when a local minimum is zero.
AR5Assertion: For equal amplitudes, Imin = 0. Reason: The two amplitudes cancel at φ = π.
Answer: A
Explanation: Both are true and the reason directly explains the result.
AR6Assertion: Path difference λ gives a dark fringe. Reason: It corresponds to phase difference 2π.
Answer: D
Explanation: The assertion is false; 2π produces a bright fringe.
AR7Assertion: Intensity is proportional to amplitude squared. Reason: The time-averaged energy flux is quadratic in field amplitude.
Answer: A
Explanation: Both are true and the reason is the physical basis.
AR8Assertion: Visibility is one for equal intensities. Reason: Imin is then zero.
Answer: A
Explanation: Both are true and Imax/Imin contrast is complete.
AR9Assertion: Closing one slit increases fringe visibility. Reason: Interference requires two overlapping coherent waves.
Answer: D
Explanation: The assertion is false; closing one slit removes interference.
AR10Assertion: The central YDSE fringe is bright for equal source phase. Reason: The central path difference is zero.
Answer: A
Explanation: Both are true and the reason gives φ = 0.
AR11Assertion: Phase difference is dimensionless. Reason: It is an angular measure expressed in radians.
Answer: A
Explanation: Both are true and the reason explains the statement.
AR12Assertion: A phase lead can be represented by +φ. Reason: The leading wave reaches a given phase earlier.
Answer: A
Explanation: Both are true.
AR13Assertion: Imax = I1 + I2 for coherent waves. Reason: The interference cross term vanishes at maximum.
Answer: D
Explanation: The assertion is false; at maximum the positive cross term is largest.
AR14Assertion: Unequal amplitudes can produce complete darkness. Reason: Imin = (a−b)².
Answer: D
Explanation: The assertion is false unless a = b; the reason is true.
AR15Assertion: Bright fringes occur at Δx = nλ. Reason: This makes φ = 2nπ.
Answer: A
Explanation: Both are true and correctly linked.
AR16Assertion: Dark fringes occur at odd half-wavelength path differences. Reason: This makes cosφ = −1.
Answer: A
Explanation: Both are true and correctly linked.
AR17Assertion: Fringe visibility depends on relative intensities. Reason: V = 2√(I1I2)/(I1+I2).
Answer: A
Explanation: Both are true and the expression proves it.
AR18Assertion: Superposition permanently changes component waves. Reason: Waves pass through each other in a linear medium.
Answer: D
Explanation: The assertion is false; the reason is true.
AR19Assertion: Coherence requires equal amplitudes. Reason: Coherence concerns phase stability, not amplitude equality.
Answer: D
Explanation: The assertion is false; the reason is true.
AR20Assertion: For equal beams, I = 4I0 cos²(φ/2). Reason: 1+cosφ = 2cos²(φ/2).
Answer: A
Explanation: Both are true and the identity gives the formula.
11
10 Case Study Questions
1. Oil-film colors
Case: White light reflects from the upper and lower surfaces of a thin oil film.
Detailed solution: Different wavelengths satisfy constructive or destructive conditions at different angles, producing colors.
Key result: Thin-film interference redistributes wavelengths spatially.
2. Noise-cancelling headphones
Case: A second sound is generated opposite in phase to ambient noise.
Detailed solution: At the ear, similar amplitudes with phase difference π give destructive interference.
Key result: The cancellation is best when amplitudes match.
3. Anti-reflection coating
Case: A coating is selected so two reflected beams cancel.
Detailed solution: Optical thickness and reflection phase shifts are chosen for odd-π relative phase.
Key result: Reduced reflection increases transmission.
4. YDSE center
Case: The observation point is equidistant from S₁ and S₂.
Detailed solution: Path difference is zero and the coherent waves arrive in phase.
Key result: A central bright fringe appears.
5. Unequal slit illumination
Case: One slit receives four times the intensity of the other.
Detailed solution: Amplitudes are in ratio 2:1; Imax = 9 units and Imin = 1 unit on a common scale.
Key result: Visibility becomes 8/10 = 0.8.
6. Monochromatic requirement
Case: A narrow spectral line is used instead of white light.
Detailed solution: A single wavelength gives a regular fixed phase-to-path relation.
Key result: Fringes are sharp and evenly interpretable.
7. Source broadening
Case: The source slit is widened substantially.
Detailed solution: Different source points form shifted fringe systems that overlap.
Key result: Spatial coherence falls and visibility decreases.
8. Path plate
Case: A thin transparent plate is placed in front of one slit.
Detailed solution: It adds optical path (μ−1)t and shifts the entire fringe pattern.
Key result: Fringe spacing stays essentially unchanged.
9. Radio antennas
Case: Two synchronized antennas radiate at the same frequency.
Detailed solution: Their fields add constructively and destructively depending on path difference.
Key result: Directional maxima and minima form.
10. Interferometer
Case: A beam is split, sent along two paths and recombined.
Detailed solution: A tiny path change creates a measurable phase shift.
Key result: Interference enables precision length and refractive-index measurements.
12
Exam Practice Banks
Academic note: These are original PYQ-pattern and exam-style questions, not verbatim reproductions of copyrighted past papers.
CBSE PYQ-Pattern Practice · 30 Questions
Q1For superposition, identify the physically correct result in an interference experiment.
Answer: A. resultant displacement equals the algebraic sum of component displacements
Explanation: resultant displacement equals the algebraic sum of component displacements. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original board derivation and structured reasoning item.
Q2For coherence, identify the physically correct result in an interference experiment.
Answer: D. coherent sources have equal frequency and constant phase difference
Explanation: coherent sources have equal frequency and constant phase difference. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original board derivation and structured reasoning item.
Q3For constructive interference, identify the physically correct result in an interference experiment.
Answer: C. Δx = nλ and φ = 2nπ
Explanation: Δx = nλ and φ = 2nπ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original board derivation and structured reasoning item.
Q4For destructive interference, identify the physically correct result in an interference experiment.
Answer: B. Δx = (2n−1)λ/2 and φ = (2n−1)π
Explanation: Δx = (2n−1)λ/2 and φ = (2n−1)π. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original board derivation and structured reasoning item.
Q5For intensity formula, identify the physically correct result in an interference experiment.
Answer: A. I = I₁+I₂+2√(I₁I₂)cosφ
Explanation: I = I₁+I₂+2√(I₁I₂)cosφ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original board derivation and structured reasoning item.
Q6For equal intensities, identify the physically correct result in an interference experiment.
Answer: D. I = 4I₀cos²(φ/2)
Explanation: I = 4I₀cos²(φ/2). The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original board derivation and structured reasoning item.
Q7For maximum intensity, identify the physically correct result in an interference experiment.
Answer: C. Imax = (a+b)²
Explanation: Imax = (a+b)². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original board derivation and structured reasoning item.
Q8For minimum intensity, identify the physically correct result in an interference experiment.
Answer: B. Imin = (a−b)²
Explanation: Imin = (a−b)². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original board derivation and structured reasoning item.
Q9For phase-path relation, identify the physically correct result in an interference experiment.
Answer: A. φ = 2πΔx/λ
Explanation: φ = 2πΔx/λ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original board derivation and structured reasoning item.
Q10For visibility, identify the physically correct result in an interference experiment.
Answer: D. V = (Imax−Imin)/(Imax+Imin)
Explanation: V = (Imax−Imin)/(Imax+Imin). The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original board derivation and structured reasoning item.
Q11For amplitude-intensity relation, identify the physically correct result in an interference experiment.
Answer: C. I₁/I₂ = a²/b²
Explanation: I₁/I₂ = a²/b². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original board derivation and structured reasoning item.
Q12For central YDSE fringe, identify the physically correct result in an interference experiment.
Answer: B. equal paths give a bright central fringe
Explanation: equal paths give a bright central fringe. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original board derivation and structured reasoning item.
Q13For energy conservation, identify the physically correct result in an interference experiment.
Answer: A. interference redistributes energy rather than creating or destroying it
Explanation: interference redistributes energy rather than creating or destroying it. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original board derivation and structured reasoning item.
Q14For source requirement, identify the physically correct result in an interference experiment.
Answer: D. one primary source illuminating two slits provides coherence
Explanation: one primary source illuminating two slits provides coherence. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original board derivation and structured reasoning item.
Q15For fringe contrast, identify the physically correct result in an interference experiment.
Answer: C. visibility is maximum when the two intensities are equal
Explanation: visibility is maximum when the two intensities are equal. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original board derivation and structured reasoning item.
Q16For superposition, identify the physically correct result in an interference experiment.
Answer: B. resultant displacement equals the algebraic sum of component displacements
Explanation: resultant displacement equals the algebraic sum of component displacements. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original board derivation and structured reasoning item.
Q17For coherence, identify the physically correct result in an interference experiment.
Answer: A. coherent sources have equal frequency and constant phase difference
Explanation: coherent sources have equal frequency and constant phase difference. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original board derivation and structured reasoning item.
Q18For constructive interference, identify the physically correct result in an interference experiment.
Answer: D. Δx = nλ and φ = 2nπ
Explanation: Δx = nλ and φ = 2nπ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original board derivation and structured reasoning item.
Q19For destructive interference, identify the physically correct result in an interference experiment.
Answer: C. Δx = (2n−1)λ/2 and φ = (2n−1)π
Explanation: Δx = (2n−1)λ/2 and φ = (2n−1)π. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original board derivation and structured reasoning item.
Q20For intensity formula, identify the physically correct result in an interference experiment.
Answer: B. I = I₁+I₂+2√(I₁I₂)cosφ
Explanation: I = I₁+I₂+2√(I₁I₂)cosφ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original board derivation and structured reasoning item.
Q21For equal intensities, identify the physically correct result in an interference experiment.
Answer: A. I = 4I₀cos²(φ/2)
Explanation: I = 4I₀cos²(φ/2). The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original board derivation and structured reasoning item.
Q22For maximum intensity, identify the physically correct result in an interference experiment.
Answer: D. Imax = (a+b)²
Explanation: Imax = (a+b)². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original board derivation and structured reasoning item.
Q23For minimum intensity, identify the physically correct result in an interference experiment.
Answer: C. Imin = (a−b)²
Explanation: Imin = (a−b)². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original board derivation and structured reasoning item.
Q24For phase-path relation, identify the physically correct result in an interference experiment.
Answer: B. φ = 2πΔx/λ
Explanation: φ = 2πΔx/λ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original board derivation and structured reasoning item.
Q25For visibility, identify the physically correct result in an interference experiment.
Answer: A. V = (Imax−Imin)/(Imax+Imin)
Explanation: V = (Imax−Imin)/(Imax+Imin). The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original board derivation and structured reasoning item.
Q26For amplitude-intensity relation, identify the physically correct result in an interference experiment.
Answer: D. I₁/I₂ = a²/b²
Explanation: I₁/I₂ = a²/b². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original board derivation and structured reasoning item.
Q27For central YDSE fringe, identify the physically correct result in an interference experiment.
Answer: C. equal paths give a bright central fringe
Explanation: equal paths give a bright central fringe. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original board derivation and structured reasoning item.
Q28For energy conservation, identify the physically correct result in an interference experiment.
Answer: B. interference redistributes energy rather than creating or destroying it
Explanation: interference redistributes energy rather than creating or destroying it. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original board derivation and structured reasoning item.
Q29For source requirement, identify the physically correct result in an interference experiment.
Answer: A. one primary source illuminating two slits provides coherence
Explanation: one primary source illuminating two slits provides coherence. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original board derivation and structured reasoning item.
Q30For fringe contrast, identify the physically correct result in an interference experiment.
Answer: D. visibility is maximum when the two intensities are equal
Explanation: visibility is maximum when the two intensities are equal. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original board derivation and structured reasoning item.
NEET PYQ-Pattern Practice · 30 Questions
Q1For superposition, identify the physically correct result in an interference experiment.
Answer: A. resultant displacement equals the algebraic sum of component displacements
Explanation: resultant displacement equals the algebraic sum of component displacements. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original single-correct conceptual selection item.
Q2For coherence, identify the physically correct result in an interference experiment.
Answer: D. coherent sources have equal frequency and constant phase difference
Explanation: coherent sources have equal frequency and constant phase difference. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original single-correct conceptual selection item.
Q3For constructive interference, identify the physically correct result in an interference experiment.
Answer: C. Δx = nλ and φ = 2nπ
Explanation: Δx = nλ and φ = 2nπ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original single-correct conceptual selection item.
Q4For destructive interference, identify the physically correct result in an interference experiment.
Answer: B. Δx = (2n−1)λ/2 and φ = (2n−1)π
Explanation: Δx = (2n−1)λ/2 and φ = (2n−1)π. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original single-correct conceptual selection item.
Q5For intensity formula, identify the physically correct result in an interference experiment.
Answer: A. I = I₁+I₂+2√(I₁I₂)cosφ
Explanation: I = I₁+I₂+2√(I₁I₂)cosφ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original single-correct conceptual selection item.
Q6For equal intensities, identify the physically correct result in an interference experiment.
Answer: D. I = 4I₀cos²(φ/2)
Explanation: I = 4I₀cos²(φ/2). The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original single-correct conceptual selection item.
Q7For maximum intensity, identify the physically correct result in an interference experiment.
Answer: C. Imax = (a+b)²
Explanation: Imax = (a+b)². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original single-correct conceptual selection item.
Q8For minimum intensity, identify the physically correct result in an interference experiment.
Answer: B. Imin = (a−b)²
Explanation: Imin = (a−b)². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original single-correct conceptual selection item.
Q9For phase-path relation, identify the physically correct result in an interference experiment.
Answer: A. φ = 2πΔx/λ
Explanation: φ = 2πΔx/λ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original single-correct conceptual selection item.
Q10For visibility, identify the physically correct result in an interference experiment.
Answer: D. V = (Imax−Imin)/(Imax+Imin)
Explanation: V = (Imax−Imin)/(Imax+Imin). The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original single-correct conceptual selection item.
Q11For amplitude-intensity relation, identify the physically correct result in an interference experiment.
Answer: C. I₁/I₂ = a²/b²
Explanation: I₁/I₂ = a²/b². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original single-correct conceptual selection item.
Q12For central YDSE fringe, identify the physically correct result in an interference experiment.
Answer: B. equal paths give a bright central fringe
Explanation: equal paths give a bright central fringe. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original single-correct conceptual selection item.
Q13For energy conservation, identify the physically correct result in an interference experiment.
Answer: A. interference redistributes energy rather than creating or destroying it
Explanation: interference redistributes energy rather than creating or destroying it. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original single-correct conceptual selection item.
Q14For source requirement, identify the physically correct result in an interference experiment.
Answer: D. one primary source illuminating two slits provides coherence
Explanation: one primary source illuminating two slits provides coherence. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original single-correct conceptual selection item.
Q15For fringe contrast, identify the physically correct result in an interference experiment.
Answer: C. visibility is maximum when the two intensities are equal
Explanation: visibility is maximum when the two intensities are equal. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original single-correct conceptual selection item.
Q16For superposition, identify the physically correct result in an interference experiment.
Answer: B. resultant displacement equals the algebraic sum of component displacements
Explanation: resultant displacement equals the algebraic sum of component displacements. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original single-correct conceptual selection item.
Q17For coherence, identify the physically correct result in an interference experiment.
Answer: A. coherent sources have equal frequency and constant phase difference
Explanation: coherent sources have equal frequency and constant phase difference. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original single-correct conceptual selection item.
Q18For constructive interference, identify the physically correct result in an interference experiment.
Answer: D. Δx = nλ and φ = 2nπ
Explanation: Δx = nλ and φ = 2nπ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original single-correct conceptual selection item.
Q19For destructive interference, identify the physically correct result in an interference experiment.
Answer: C. Δx = (2n−1)λ/2 and φ = (2n−1)π
Explanation: Δx = (2n−1)λ/2 and φ = (2n−1)π. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original single-correct conceptual selection item.
Q20For intensity formula, identify the physically correct result in an interference experiment.
Answer: B. I = I₁+I₂+2√(I₁I₂)cosφ
Explanation: I = I₁+I₂+2√(I₁I₂)cosφ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original single-correct conceptual selection item.
Q21For equal intensities, identify the physically correct result in an interference experiment.
Answer: A. I = 4I₀cos²(φ/2)
Explanation: I = 4I₀cos²(φ/2). The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original single-correct conceptual selection item.
Q22For maximum intensity, identify the physically correct result in an interference experiment.
Answer: D. Imax = (a+b)²
Explanation: Imax = (a+b)². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original single-correct conceptual selection item.
Q23For minimum intensity, identify the physically correct result in an interference experiment.
Answer: C. Imin = (a−b)²
Explanation: Imin = (a−b)². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original single-correct conceptual selection item.
Q24For phase-path relation, identify the physically correct result in an interference experiment.
Answer: B. φ = 2πΔx/λ
Explanation: φ = 2πΔx/λ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original single-correct conceptual selection item.
Q25For visibility, identify the physically correct result in an interference experiment.
Answer: A. V = (Imax−Imin)/(Imax+Imin)
Explanation: V = (Imax−Imin)/(Imax+Imin). The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original single-correct conceptual selection item.
Q26For amplitude-intensity relation, identify the physically correct result in an interference experiment.
Answer: D. I₁/I₂ = a²/b²
Explanation: I₁/I₂ = a²/b². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original single-correct conceptual selection item.
Q27For central YDSE fringe, identify the physically correct result in an interference experiment.
Answer: C. equal paths give a bright central fringe
Explanation: equal paths give a bright central fringe. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original single-correct conceptual selection item.
Q28For energy conservation, identify the physically correct result in an interference experiment.
Answer: B. interference redistributes energy rather than creating or destroying it
Explanation: interference redistributes energy rather than creating or destroying it. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original single-correct conceptual selection item.
Q29For source requirement, identify the physically correct result in an interference experiment.
Answer: A. one primary source illuminating two slits provides coherence
Explanation: one primary source illuminating two slits provides coherence. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original single-correct conceptual selection item.
Q30For fringe contrast, identify the physically correct result in an interference experiment.
Answer: D. visibility is maximum when the two intensities are equal
Explanation: visibility is maximum when the two intensities are equal. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original single-correct conceptual selection item.
JEE Main PYQ-Pattern Practice · 30 Questions
Q1For superposition, identify the physically correct result in an interference experiment.
Answer: A. resultant displacement equals the algebraic sum of component displacements
Explanation: resultant displacement equals the algebraic sum of component displacements. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original short numerical and formula application item.
Q2For coherence, identify the physically correct result in an interference experiment.
Answer: D. coherent sources have equal frequency and constant phase difference
Explanation: coherent sources have equal frequency and constant phase difference. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original short numerical and formula application item.
Q3For constructive interference, identify the physically correct result in an interference experiment.
Answer: C. Δx = nλ and φ = 2nπ
Explanation: Δx = nλ and φ = 2nπ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original short numerical and formula application item.
Q4For destructive interference, identify the physically correct result in an interference experiment.
Answer: B. Δx = (2n−1)λ/2 and φ = (2n−1)π
Explanation: Δx = (2n−1)λ/2 and φ = (2n−1)π. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original short numerical and formula application item.
Q5For intensity formula, identify the physically correct result in an interference experiment.
Answer: A. I = I₁+I₂+2√(I₁I₂)cosφ
Explanation: I = I₁+I₂+2√(I₁I₂)cosφ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original short numerical and formula application item.
Q6For equal intensities, identify the physically correct result in an interference experiment.
Answer: D. I = 4I₀cos²(φ/2)
Explanation: I = 4I₀cos²(φ/2). The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original short numerical and formula application item.
Q7For maximum intensity, identify the physically correct result in an interference experiment.
Answer: C. Imax = (a+b)²
Explanation: Imax = (a+b)². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original short numerical and formula application item.
Q8For minimum intensity, identify the physically correct result in an interference experiment.
Answer: B. Imin = (a−b)²
Explanation: Imin = (a−b)². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original short numerical and formula application item.
Q9For phase-path relation, identify the physically correct result in an interference experiment.
Answer: A. φ = 2πΔx/λ
Explanation: φ = 2πΔx/λ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original short numerical and formula application item.
Q10For visibility, identify the physically correct result in an interference experiment.
Answer: D. V = (Imax−Imin)/(Imax+Imin)
Explanation: V = (Imax−Imin)/(Imax+Imin). The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original short numerical and formula application item.
Q11For amplitude-intensity relation, identify the physically correct result in an interference experiment.
Answer: C. I₁/I₂ = a²/b²
Explanation: I₁/I₂ = a²/b². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original short numerical and formula application item.
Q12For central YDSE fringe, identify the physically correct result in an interference experiment.
Answer: B. equal paths give a bright central fringe
Explanation: equal paths give a bright central fringe. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original short numerical and formula application item.
Q13For energy conservation, identify the physically correct result in an interference experiment.
Answer: A. interference redistributes energy rather than creating or destroying it
Explanation: interference redistributes energy rather than creating or destroying it. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original short numerical and formula application item.
Q14For source requirement, identify the physically correct result in an interference experiment.
Answer: D. one primary source illuminating two slits provides coherence
Explanation: one primary source illuminating two slits provides coherence. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original short numerical and formula application item.
Q15For fringe contrast, identify the physically correct result in an interference experiment.
Answer: C. visibility is maximum when the two intensities are equal
Explanation: visibility is maximum when the two intensities are equal. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original short numerical and formula application item.
Q16For superposition, identify the physically correct result in an interference experiment.
Answer: B. resultant displacement equals the algebraic sum of component displacements
Explanation: resultant displacement equals the algebraic sum of component displacements. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original short numerical and formula application item.
Q17For coherence, identify the physically correct result in an interference experiment.
Answer: A. coherent sources have equal frequency and constant phase difference
Explanation: coherent sources have equal frequency and constant phase difference. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original short numerical and formula application item.
Q18For constructive interference, identify the physically correct result in an interference experiment.
Answer: D. Δx = nλ and φ = 2nπ
Explanation: Δx = nλ and φ = 2nπ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original short numerical and formula application item.
Q19For destructive interference, identify the physically correct result in an interference experiment.
Answer: C. Δx = (2n−1)λ/2 and φ = (2n−1)π
Explanation: Δx = (2n−1)λ/2 and φ = (2n−1)π. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original short numerical and formula application item.
Q20For intensity formula, identify the physically correct result in an interference experiment.
Answer: B. I = I₁+I₂+2√(I₁I₂)cosφ
Explanation: I = I₁+I₂+2√(I₁I₂)cosφ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original short numerical and formula application item.
Q21For equal intensities, identify the physically correct result in an interference experiment.
Answer: A. I = 4I₀cos²(φ/2)
Explanation: I = 4I₀cos²(φ/2). The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original short numerical and formula application item.
Q22For maximum intensity, identify the physically correct result in an interference experiment.
Answer: D. Imax = (a+b)²
Explanation: Imax = (a+b)². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original short numerical and formula application item.
Q23For minimum intensity, identify the physically correct result in an interference experiment.
Answer: C. Imin = (a−b)²
Explanation: Imin = (a−b)². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original short numerical and formula application item.
Q24For phase-path relation, identify the physically correct result in an interference experiment.
Answer: B. φ = 2πΔx/λ
Explanation: φ = 2πΔx/λ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original short numerical and formula application item.
Q25For visibility, identify the physically correct result in an interference experiment.
Answer: A. V = (Imax−Imin)/(Imax+Imin)
Explanation: V = (Imax−Imin)/(Imax+Imin). The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original short numerical and formula application item.
Q26For amplitude-intensity relation, identify the physically correct result in an interference experiment.
Answer: D. I₁/I₂ = a²/b²
Explanation: I₁/I₂ = a²/b². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original short numerical and formula application item.
Q27For central YDSE fringe, identify the physically correct result in an interference experiment.
Answer: C. equal paths give a bright central fringe
Explanation: equal paths give a bright central fringe. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original short numerical and formula application item.
Q28For energy conservation, identify the physically correct result in an interference experiment.
Answer: B. interference redistributes energy rather than creating or destroying it
Explanation: interference redistributes energy rather than creating or destroying it. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original short numerical and formula application item.
Q29For source requirement, identify the physically correct result in an interference experiment.
Answer: A. one primary source illuminating two slits provides coherence
Explanation: one primary source illuminating two slits provides coherence. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original short numerical and formula application item.
Q30For fringe contrast, identify the physically correct result in an interference experiment.
Answer: D. visibility is maximum when the two intensities are equal
Explanation: visibility is maximum when the two intensities are equal. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original short numerical and formula application item.
JEE Advanced PYQ-Pattern Practice · 30 Questions
Q1For superposition, identify the physically correct result in an interference experiment.
Answer: A. resultant displacement equals the algebraic sum of component displacements
Explanation: resultant displacement equals the algebraic sum of component displacements. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original multi-concept interference reasoning item.
Q2For coherence, identify the physically correct result in an interference experiment.
Answer: D. coherent sources have equal frequency and constant phase difference
Explanation: coherent sources have equal frequency and constant phase difference. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original multi-concept interference reasoning item.
Q3For constructive interference, identify the physically correct result in an interference experiment.
Answer: C. Δx = nλ and φ = 2nπ
Explanation: Δx = nλ and φ = 2nπ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original multi-concept interference reasoning item.
Q4For destructive interference, identify the physically correct result in an interference experiment.
Answer: B. Δx = (2n−1)λ/2 and φ = (2n−1)π
Explanation: Δx = (2n−1)λ/2 and φ = (2n−1)π. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original multi-concept interference reasoning item.
Q5For intensity formula, identify the physically correct result in an interference experiment.
Answer: A. I = I₁+I₂+2√(I₁I₂)cosφ
Explanation: I = I₁+I₂+2√(I₁I₂)cosφ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original multi-concept interference reasoning item.
Q6For equal intensities, identify the physically correct result in an interference experiment.
Answer: D. I = 4I₀cos²(φ/2)
Explanation: I = 4I₀cos²(φ/2). The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original multi-concept interference reasoning item.
Q7For maximum intensity, identify the physically correct result in an interference experiment.
Answer: C. Imax = (a+b)²
Explanation: Imax = (a+b)². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original multi-concept interference reasoning item.
Q8For minimum intensity, identify the physically correct result in an interference experiment.
Answer: B. Imin = (a−b)²
Explanation: Imin = (a−b)². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original multi-concept interference reasoning item.
Q9For phase-path relation, identify the physically correct result in an interference experiment.
Answer: A. φ = 2πΔx/λ
Explanation: φ = 2πΔx/λ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original multi-concept interference reasoning item.
Q10For visibility, identify the physically correct result in an interference experiment.
Answer: D. V = (Imax−Imin)/(Imax+Imin)
Explanation: V = (Imax−Imin)/(Imax+Imin). The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original multi-concept interference reasoning item.
Q11For amplitude-intensity relation, identify the physically correct result in an interference experiment.
Answer: C. I₁/I₂ = a²/b²
Explanation: I₁/I₂ = a²/b². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original multi-concept interference reasoning item.
Q12For central YDSE fringe, identify the physically correct result in an interference experiment.
Answer: B. equal paths give a bright central fringe
Explanation: equal paths give a bright central fringe. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original multi-concept interference reasoning item.
Q13For energy conservation, identify the physically correct result in an interference experiment.
Answer: A. interference redistributes energy rather than creating or destroying it
Explanation: interference redistributes energy rather than creating or destroying it. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original multi-concept interference reasoning item.
Q14For source requirement, identify the physically correct result in an interference experiment.
Answer: D. one primary source illuminating two slits provides coherence
Explanation: one primary source illuminating two slits provides coherence. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original multi-concept interference reasoning item.
Q15For fringe contrast, identify the physically correct result in an interference experiment.
Answer: C. visibility is maximum when the two intensities are equal
Explanation: visibility is maximum when the two intensities are equal. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original multi-concept interference reasoning item.
Q16For superposition, identify the physically correct result in an interference experiment.
Answer: B. resultant displacement equals the algebraic sum of component displacements
Explanation: resultant displacement equals the algebraic sum of component displacements. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original multi-concept interference reasoning item.
Q17For coherence, identify the physically correct result in an interference experiment.
Answer: A. coherent sources have equal frequency and constant phase difference
Explanation: coherent sources have equal frequency and constant phase difference. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original multi-concept interference reasoning item.
Q18For constructive interference, identify the physically correct result in an interference experiment.
Answer: D. Δx = nλ and φ = 2nπ
Explanation: Δx = nλ and φ = 2nπ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original multi-concept interference reasoning item.
Q19For destructive interference, identify the physically correct result in an interference experiment.
Answer: C. Δx = (2n−1)λ/2 and φ = (2n−1)π
Explanation: Δx = (2n−1)λ/2 and φ = (2n−1)π. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original multi-concept interference reasoning item.
Q20For intensity formula, identify the physically correct result in an interference experiment.
Answer: B. I = I₁+I₂+2√(I₁I₂)cosφ
Explanation: I = I₁+I₂+2√(I₁I₂)cosφ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original multi-concept interference reasoning item.
Q21For equal intensities, identify the physically correct result in an interference experiment.
Answer: A. I = 4I₀cos²(φ/2)
Explanation: I = 4I₀cos²(φ/2). The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original multi-concept interference reasoning item.
Q22For maximum intensity, identify the physically correct result in an interference experiment.
Answer: D. Imax = (a+b)²
Explanation: Imax = (a+b)². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original multi-concept interference reasoning item.
Q23For minimum intensity, identify the physically correct result in an interference experiment.
Answer: C. Imin = (a−b)²
Explanation: Imin = (a−b)². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original multi-concept interference reasoning item.
Q24For phase-path relation, identify the physically correct result in an interference experiment.
Answer: B. φ = 2πΔx/λ
Explanation: φ = 2πΔx/λ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original multi-concept interference reasoning item.
Q25For visibility, identify the physically correct result in an interference experiment.
Answer: A. V = (Imax−Imin)/(Imax+Imin)
Explanation: V = (Imax−Imin)/(Imax+Imin). The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original multi-concept interference reasoning item.
Q26For amplitude-intensity relation, identify the physically correct result in an interference experiment.
Answer: D. I₁/I₂ = a²/b²
Explanation: I₁/I₂ = a²/b². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original multi-concept interference reasoning item.
Q27For central YDSE fringe, identify the physically correct result in an interference experiment.
Answer: C. equal paths give a bright central fringe
Explanation: equal paths give a bright central fringe. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original multi-concept interference reasoning item.
Q28For energy conservation, identify the physically correct result in an interference experiment.
Answer: B. interference redistributes energy rather than creating or destroying it
Explanation: interference redistributes energy rather than creating or destroying it. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original multi-concept interference reasoning item.
Q29For source requirement, identify the physically correct result in an interference experiment.
Answer: A. one primary source illuminating two slits provides coherence
Explanation: one primary source illuminating two slits provides coherence. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original multi-concept interference reasoning item.
Q30For fringe contrast, identify the physically correct result in an interference experiment.
Answer: D. visibility is maximum when the two intensities are equal
Explanation: visibility is maximum when the two intensities are equal. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original multi-concept interference reasoning item.
IB Physics Exam-Style Questions · 30 Questions
Q1For superposition, identify the physically correct result in an interference experiment.
Answer: A. resultant displacement equals the algebraic sum of component displacements
Explanation: resultant displacement equals the algebraic sum of component displacements. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original explain, calculate and evaluate item.
Q2For coherence, identify the physically correct result in an interference experiment.
Answer: D. coherent sources have equal frequency and constant phase difference
Explanation: coherent sources have equal frequency and constant phase difference. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original explain, calculate and evaluate item.
Q3For constructive interference, identify the physically correct result in an interference experiment.
Answer: C. Δx = nλ and φ = 2nπ
Explanation: Δx = nλ and φ = 2nπ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original explain, calculate and evaluate item.
Q4For destructive interference, identify the physically correct result in an interference experiment.
Answer: B. Δx = (2n−1)λ/2 and φ = (2n−1)π
Explanation: Δx = (2n−1)λ/2 and φ = (2n−1)π. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original explain, calculate and evaluate item.
Q5For intensity formula, identify the physically correct result in an interference experiment.
Answer: A. I = I₁+I₂+2√(I₁I₂)cosφ
Explanation: I = I₁+I₂+2√(I₁I₂)cosφ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original explain, calculate and evaluate item.
Q6For equal intensities, identify the physically correct result in an interference experiment.
Answer: D. I = 4I₀cos²(φ/2)
Explanation: I = 4I₀cos²(φ/2). The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original explain, calculate and evaluate item.
Q7For maximum intensity, identify the physically correct result in an interference experiment.
Answer: C. Imax = (a+b)²
Explanation: Imax = (a+b)². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original explain, calculate and evaluate item.
Q8For minimum intensity, identify the physically correct result in an interference experiment.
Answer: B. Imin = (a−b)²
Explanation: Imin = (a−b)². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original explain, calculate and evaluate item.
Q9For phase-path relation, identify the physically correct result in an interference experiment.
Answer: A. φ = 2πΔx/λ
Explanation: φ = 2πΔx/λ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original explain, calculate and evaluate item.
Q10For visibility, identify the physically correct result in an interference experiment.
Answer: D. V = (Imax−Imin)/(Imax+Imin)
Explanation: V = (Imax−Imin)/(Imax+Imin). The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original explain, calculate and evaluate item.
Q11For amplitude-intensity relation, identify the physically correct result in an interference experiment.
Answer: C. I₁/I₂ = a²/b²
Explanation: I₁/I₂ = a²/b². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original explain, calculate and evaluate item.
Q12For central YDSE fringe, identify the physically correct result in an interference experiment.
Answer: B. equal paths give a bright central fringe
Explanation: equal paths give a bright central fringe. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original explain, calculate and evaluate item.
Q13For energy conservation, identify the physically correct result in an interference experiment.
Answer: A. interference redistributes energy rather than creating or destroying it
Explanation: interference redistributes energy rather than creating or destroying it. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original explain, calculate and evaluate item.
Q14For source requirement, identify the physically correct result in an interference experiment.
Answer: D. one primary source illuminating two slits provides coherence
Explanation: one primary source illuminating two slits provides coherence. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original explain, calculate and evaluate item.
Q15For fringe contrast, identify the physically correct result in an interference experiment.
Answer: C. visibility is maximum when the two intensities are equal
Explanation: visibility is maximum when the two intensities are equal. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original explain, calculate and evaluate item.
Q16For superposition, identify the physically correct result in an interference experiment.
Answer: B. resultant displacement equals the algebraic sum of component displacements
Explanation: resultant displacement equals the algebraic sum of component displacements. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original explain, calculate and evaluate item.
Q17For coherence, identify the physically correct result in an interference experiment.
Answer: A. coherent sources have equal frequency and constant phase difference
Explanation: coherent sources have equal frequency and constant phase difference. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original explain, calculate and evaluate item.
Q18For constructive interference, identify the physically correct result in an interference experiment.
Answer: D. Δx = nλ and φ = 2nπ
Explanation: Δx = nλ and φ = 2nπ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original explain, calculate and evaluate item.
Q19For destructive interference, identify the physically correct result in an interference experiment.
Answer: C. Δx = (2n−1)λ/2 and φ = (2n−1)π
Explanation: Δx = (2n−1)λ/2 and φ = (2n−1)π. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original explain, calculate and evaluate item.
Q20For intensity formula, identify the physically correct result in an interference experiment.
Answer: B. I = I₁+I₂+2√(I₁I₂)cosφ
Explanation: I = I₁+I₂+2√(I₁I₂)cosφ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original explain, calculate and evaluate item.
Q21For equal intensities, identify the physically correct result in an interference experiment.
Answer: A. I = 4I₀cos²(φ/2)
Explanation: I = 4I₀cos²(φ/2). The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original explain, calculate and evaluate item.
Q22For maximum intensity, identify the physically correct result in an interference experiment.
Answer: D. Imax = (a+b)²
Explanation: Imax = (a+b)². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original explain, calculate and evaluate item.
Q23For minimum intensity, identify the physically correct result in an interference experiment.
Answer: C. Imin = (a−b)²
Explanation: Imin = (a−b)². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original explain, calculate and evaluate item.
Q24For phase-path relation, identify the physically correct result in an interference experiment.
Answer: B. φ = 2πΔx/λ
Explanation: φ = 2πΔx/λ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original explain, calculate and evaluate item.
Q25For visibility, identify the physically correct result in an interference experiment.
Answer: A. V = (Imax−Imin)/(Imax+Imin)
Explanation: V = (Imax−Imin)/(Imax+Imin). The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original explain, calculate and evaluate item.
Q26For amplitude-intensity relation, identify the physically correct result in an interference experiment.
Answer: D. I₁/I₂ = a²/b²
Explanation: I₁/I₂ = a²/b². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original explain, calculate and evaluate item.
Q27For central YDSE fringe, identify the physically correct result in an interference experiment.
Answer: C. equal paths give a bright central fringe
Explanation: equal paths give a bright central fringe. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original explain, calculate and evaluate item.
Q28For energy conservation, identify the physically correct result in an interference experiment.
Answer: B. interference redistributes energy rather than creating or destroying it
Explanation: interference redistributes energy rather than creating or destroying it. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original explain, calculate and evaluate item.
Q29For source requirement, identify the physically correct result in an interference experiment.
Answer: A. one primary source illuminating two slits provides coherence
Explanation: one primary source illuminating two slits provides coherence. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original explain, calculate and evaluate item.
Q30For fringe contrast, identify the physically correct result in an interference experiment.
Answer: D. visibility is maximum when the two intensities are equal
Explanation: visibility is maximum when the two intensities are equal. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original explain, calculate and evaluate item.
IGCSE Exam-Style Questions · 30 Questions
Q1For superposition, identify the physically correct result in an interference experiment.
Answer: A. resultant displacement equals the algebraic sum of component displacements
Explanation: resultant displacement equals the algebraic sum of component displacements. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original clear wave interpretation and application item.
Q2For coherence, identify the physically correct result in an interference experiment.
Answer: D. coherent sources have equal frequency and constant phase difference
Explanation: coherent sources have equal frequency and constant phase difference. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original clear wave interpretation and application item.
Q3For constructive interference, identify the physically correct result in an interference experiment.
Answer: C. Δx = nλ and φ = 2nπ
Explanation: Δx = nλ and φ = 2nπ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original clear wave interpretation and application item.
Q4For destructive interference, identify the physically correct result in an interference experiment.
Answer: B. Δx = (2n−1)λ/2 and φ = (2n−1)π
Explanation: Δx = (2n−1)λ/2 and φ = (2n−1)π. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original clear wave interpretation and application item.
Q5For intensity formula, identify the physically correct result in an interference experiment.
Answer: A. I = I₁+I₂+2√(I₁I₂)cosφ
Explanation: I = I₁+I₂+2√(I₁I₂)cosφ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original clear wave interpretation and application item.
Q6For equal intensities, identify the physically correct result in an interference experiment.
Answer: D. I = 4I₀cos²(φ/2)
Explanation: I = 4I₀cos²(φ/2). The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original clear wave interpretation and application item.
Q7For maximum intensity, identify the physically correct result in an interference experiment.
Answer: C. Imax = (a+b)²
Explanation: Imax = (a+b)². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original clear wave interpretation and application item.
Q8For minimum intensity, identify the physically correct result in an interference experiment.
Answer: B. Imin = (a−b)²
Explanation: Imin = (a−b)². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original clear wave interpretation and application item.
Q9For phase-path relation, identify the physically correct result in an interference experiment.
Answer: A. φ = 2πΔx/λ
Explanation: φ = 2πΔx/λ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original clear wave interpretation and application item.
Q10For visibility, identify the physically correct result in an interference experiment.
Answer: D. V = (Imax−Imin)/(Imax+Imin)
Explanation: V = (Imax−Imin)/(Imax+Imin). The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original clear wave interpretation and application item.
Q11For amplitude-intensity relation, identify the physically correct result in an interference experiment.
Answer: C. I₁/I₂ = a²/b²
Explanation: I₁/I₂ = a²/b². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original clear wave interpretation and application item.
Q12For central YDSE fringe, identify the physically correct result in an interference experiment.
Answer: B. equal paths give a bright central fringe
Explanation: equal paths give a bright central fringe. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original clear wave interpretation and application item.
Q13For energy conservation, identify the physically correct result in an interference experiment.
Answer: A. interference redistributes energy rather than creating or destroying it
Explanation: interference redistributes energy rather than creating or destroying it. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original clear wave interpretation and application item.
Q14For source requirement, identify the physically correct result in an interference experiment.
Answer: D. one primary source illuminating two slits provides coherence
Explanation: one primary source illuminating two slits provides coherence. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original clear wave interpretation and application item.
Q15For fringe contrast, identify the physically correct result in an interference experiment.
Answer: C. visibility is maximum when the two intensities are equal
Explanation: visibility is maximum when the two intensities are equal. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original clear wave interpretation and application item.
Q16For superposition, identify the physically correct result in an interference experiment.
Answer: B. resultant displacement equals the algebraic sum of component displacements
Explanation: resultant displacement equals the algebraic sum of component displacements. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original clear wave interpretation and application item.
Q17For coherence, identify the physically correct result in an interference experiment.
Answer: A. coherent sources have equal frequency and constant phase difference
Explanation: coherent sources have equal frequency and constant phase difference. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original clear wave interpretation and application item.
Q18For constructive interference, identify the physically correct result in an interference experiment.
Answer: D. Δx = nλ and φ = 2nπ
Explanation: Δx = nλ and φ = 2nπ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original clear wave interpretation and application item.
Q19For destructive interference, identify the physically correct result in an interference experiment.
Answer: C. Δx = (2n−1)λ/2 and φ = (2n−1)π
Explanation: Δx = (2n−1)λ/2 and φ = (2n−1)π. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original clear wave interpretation and application item.
Q20For intensity formula, identify the physically correct result in an interference experiment.
Answer: B. I = I₁+I₂+2√(I₁I₂)cosφ
Explanation: I = I₁+I₂+2√(I₁I₂)cosφ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original clear wave interpretation and application item.
Q21For equal intensities, identify the physically correct result in an interference experiment.
Answer: A. I = 4I₀cos²(φ/2)
Explanation: I = 4I₀cos²(φ/2). The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original clear wave interpretation and application item.
Q22For maximum intensity, identify the physically correct result in an interference experiment.
Answer: D. Imax = (a+b)²
Explanation: Imax = (a+b)². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original clear wave interpretation and application item.
Q23For minimum intensity, identify the physically correct result in an interference experiment.
Answer: C. Imin = (a−b)²
Explanation: Imin = (a−b)². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original clear wave interpretation and application item.
Q24For phase-path relation, identify the physically correct result in an interference experiment.
Answer: B. φ = 2πΔx/λ
Explanation: φ = 2πΔx/λ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original clear wave interpretation and application item.
Q25For visibility, identify the physically correct result in an interference experiment.
Answer: A. V = (Imax−Imin)/(Imax+Imin)
Explanation: V = (Imax−Imin)/(Imax+Imin). The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original clear wave interpretation and application item.
Q26For amplitude-intensity relation, identify the physically correct result in an interference experiment.
Answer: D. I₁/I₂ = a²/b²
Explanation: I₁/I₂ = a²/b². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original clear wave interpretation and application item.
Q27For central YDSE fringe, identify the physically correct result in an interference experiment.
Answer: C. equal paths give a bright central fringe
Explanation: equal paths give a bright central fringe. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original clear wave interpretation and application item.
Q28For energy conservation, identify the physically correct result in an interference experiment.
Answer: B. interference redistributes energy rather than creating or destroying it
Explanation: interference redistributes energy rather than creating or destroying it. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original clear wave interpretation and application item.
Q29For source requirement, identify the physically correct result in an interference experiment.
Answer: A. one primary source illuminating two slits provides coherence
Explanation: one primary source illuminating two slits provides coherence. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original clear wave interpretation and application item.
Q30For fringe contrast, identify the physically correct result in an interference experiment.
Answer: D. visibility is maximum when the two intensities are equal
Explanation: visibility is maximum when the two intensities are equal. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original clear wave interpretation and application item.
A-Level Exam-Style Questions · 30 Questions
Q1For superposition, identify the physically correct result in an interference experiment.
Answer: A. resultant displacement equals the algebraic sum of component displacements
Explanation: resultant displacement equals the algebraic sum of component displacements. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original structured derivation and quantitative analysis item.
Q2For coherence, identify the physically correct result in an interference experiment.
Answer: D. coherent sources have equal frequency and constant phase difference
Explanation: coherent sources have equal frequency and constant phase difference. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original structured derivation and quantitative analysis item.
Q3For constructive interference, identify the physically correct result in an interference experiment.
Answer: C. Δx = nλ and φ = 2nπ
Explanation: Δx = nλ and φ = 2nπ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original structured derivation and quantitative analysis item.
Q4For destructive interference, identify the physically correct result in an interference experiment.
Answer: B. Δx = (2n−1)λ/2 and φ = (2n−1)π
Explanation: Δx = (2n−1)λ/2 and φ = (2n−1)π. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original structured derivation and quantitative analysis item.
Q5For intensity formula, identify the physically correct result in an interference experiment.
Answer: A. I = I₁+I₂+2√(I₁I₂)cosφ
Explanation: I = I₁+I₂+2√(I₁I₂)cosφ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original structured derivation and quantitative analysis item.
Q6For equal intensities, identify the physically correct result in an interference experiment.
Answer: D. I = 4I₀cos²(φ/2)
Explanation: I = 4I₀cos²(φ/2). The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original structured derivation and quantitative analysis item.
Q7For maximum intensity, identify the physically correct result in an interference experiment.
Answer: C. Imax = (a+b)²
Explanation: Imax = (a+b)². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original structured derivation and quantitative analysis item.
Q8For minimum intensity, identify the physically correct result in an interference experiment.
Answer: B. Imin = (a−b)²
Explanation: Imin = (a−b)². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original structured derivation and quantitative analysis item.
Q9For phase-path relation, identify the physically correct result in an interference experiment.
Answer: A. φ = 2πΔx/λ
Explanation: φ = 2πΔx/λ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original structured derivation and quantitative analysis item.
Q10For visibility, identify the physically correct result in an interference experiment.
Answer: D. V = (Imax−Imin)/(Imax+Imin)
Explanation: V = (Imax−Imin)/(Imax+Imin). The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original structured derivation and quantitative analysis item.
Q11For amplitude-intensity relation, identify the physically correct result in an interference experiment.
Answer: C. I₁/I₂ = a²/b²
Explanation: I₁/I₂ = a²/b². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original structured derivation and quantitative analysis item.
Q12For central YDSE fringe, identify the physically correct result in an interference experiment.
Answer: B. equal paths give a bright central fringe
Explanation: equal paths give a bright central fringe. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original structured derivation and quantitative analysis item.
Q13For energy conservation, identify the physically correct result in an interference experiment.
Answer: A. interference redistributes energy rather than creating or destroying it
Explanation: interference redistributes energy rather than creating or destroying it. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original structured derivation and quantitative analysis item.
Q14For source requirement, identify the physically correct result in an interference experiment.
Answer: D. one primary source illuminating two slits provides coherence
Explanation: one primary source illuminating two slits provides coherence. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original structured derivation and quantitative analysis item.
Q15For fringe contrast, identify the physically correct result in an interference experiment.
Answer: C. visibility is maximum when the two intensities are equal
Explanation: visibility is maximum when the two intensities are equal. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original structured derivation and quantitative analysis item.
Q16For superposition, identify the physically correct result in an interference experiment.
Answer: B. resultant displacement equals the algebraic sum of component displacements
Explanation: resultant displacement equals the algebraic sum of component displacements. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original structured derivation and quantitative analysis item.
Q17For coherence, identify the physically correct result in an interference experiment.
Answer: A. coherent sources have equal frequency and constant phase difference
Explanation: coherent sources have equal frequency and constant phase difference. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original structured derivation and quantitative analysis item.
Q18For constructive interference, identify the physically correct result in an interference experiment.
Answer: D. Δx = nλ and φ = 2nπ
Explanation: Δx = nλ and φ = 2nπ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original structured derivation and quantitative analysis item.
Q19For destructive interference, identify the physically correct result in an interference experiment.
Answer: C. Δx = (2n−1)λ/2 and φ = (2n−1)π
Explanation: Δx = (2n−1)λ/2 and φ = (2n−1)π. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original structured derivation and quantitative analysis item.
Q20For intensity formula, identify the physically correct result in an interference experiment.
Answer: B. I = I₁+I₂+2√(I₁I₂)cosφ
Explanation: I = I₁+I₂+2√(I₁I₂)cosφ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original structured derivation and quantitative analysis item.
Q21For equal intensities, identify the physically correct result in an interference experiment.
Answer: A. I = 4I₀cos²(φ/2)
Explanation: I = 4I₀cos²(φ/2). The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original structured derivation and quantitative analysis item.
Q22For maximum intensity, identify the physically correct result in an interference experiment.
Answer: D. Imax = (a+b)²
Explanation: Imax = (a+b)². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original structured derivation and quantitative analysis item.
Q23For minimum intensity, identify the physically correct result in an interference experiment.
Answer: C. Imin = (a−b)²
Explanation: Imin = (a−b)². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original structured derivation and quantitative analysis item.
Q24For phase-path relation, identify the physically correct result in an interference experiment.
Answer: B. φ = 2πΔx/λ
Explanation: φ = 2πΔx/λ. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original structured derivation and quantitative analysis item.
Q25For visibility, identify the physically correct result in an interference experiment.
Answer: A. V = (Imax−Imin)/(Imax+Imin)
Explanation: V = (Imax−Imin)/(Imax+Imin). The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original structured derivation and quantitative analysis item.
Q26For amplitude-intensity relation, identify the physically correct result in an interference experiment.
Answer: D. I₁/I₂ = a²/b²
Explanation: I₁/I₂ = a²/b². The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original structured derivation and quantitative analysis item.
Q27For central YDSE fringe, identify the physically correct result in an interference experiment.
Answer: C. equal paths give a bright central fringe
Explanation: equal paths give a bright central fringe. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original structured derivation and quantitative analysis item.
Q28For energy conservation, identify the physically correct result in an interference experiment.
Answer: B. interference redistributes energy rather than creating or destroying it
Explanation: interference redistributes energy rather than creating or destroying it. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original structured derivation and quantitative analysis item.
Q29For source requirement, identify the physically correct result in an interference experiment.
Answer: A. one primary source illuminating two slits provides coherence
Explanation: one primary source illuminating two slits provides coherence. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original structured derivation and quantitative analysis item.
Q30For fringe contrast, identify the physically correct result in an interference experiment.
Answer: D. visibility is maximum when the two intensities are equal
Explanation: visibility is maximum when the two intensities are equal. The other statements conflict with superposition, coherence, or the amplitude-squared law. This is an original structured derivation and quantitative analysis item.
13
Quick Revision
Core Formula
I = I₁+I₂+2√(I₁I₂)cosφ
Bright Condition
φ = 2nπ; Δx = nλ
Dark Condition
φ = (2n−1)π; Δx = (2n−1)λ/2
Equal Beams
I = 4I₀cos²(φ/2); Imax = 4I₀; Imin = 0
Amplitude Ratio
I₁/I₂ = a²/b²
Common Trap
Coherence requires constant phase difference, not equal amplitude.
Kumar Sir Exam Tips
- Always use small a and b for amplitudes in this derivation.
- Write the cross term 2√(I₁I₂)cosφ carefully.
- Path difference λ gives a bright, not dark, fringe.
- Complete darkness requires equal amplitudes.
- Coherence means same frequency and constant phase difference.
- Draw YDSE labels d, D and β clearly in board answers.