Definition
Coherent sources
Two sources are coherent if they emit waves of the same frequency with a constant phase difference. Coherence is necessary for sustained interference patterns.
-- NCERT Class 12 Physics, Ch. 10, p. 264Coherent Sources
8 MCQs8-step worked example
Source: NCERT OpticsOfficial key: NTA-verifiedLast updated: 27 Sep 2026
Coherent Sources, explained for NEET
Two torches pointed at the same wall never produce fringes. Two slits lit by one lamp do. The difference is not brightness and not wavelength — it is whether the phase difference between the two arriving waves stays fixed in time.
NCERT Class 12 Physics Chapter 10, page 264, defines coherent sources as sources whose phase difference at any point remains constant with time. Read that definition carefully: it does not say the phase difference is zero. Two slits fed by the same wavefront can sit at different distances from a point on the screen, so the phase difference there is large — but it does not change, so the fringe at that point stays put and is visible. That constancy, not equality, is what "sustained interference" means.
Independent sources fail this test for a physical reason worth naming. Light from an ordinary source is emitted in wave trains whose phase resets in times of the order of 10⁻¹⁰ s, each train with a random starting phase. Two independent lamps therefore reshuffle their relative phase about 10⁸ times a second. Interference still occurs at every instant; the maxima simply move faster than any eye or detector can follow, so what you record is the sum of the two intensities with the cross term averaged to zero. Uniform illumination, no fringes.
This is why the double-slit arrangement puts one source behind both slits. The two slits are not sources in their own right — they are two windows onto the same wavefront, so whatever random phase jump the parent source makes, both slits make it together and the difference between them never changes.
Two conditions are often confused with coherence and are separate requirements: the sources must be monochromatic (or nearly so) for sharp fringes, and their amplitudes should be comparable for good contrast. Neither creates coherence; both affect how clearly an already-sustained pattern is seen.
Watch out for questions that offer "two identical sodium lamps" or "two sources of the same wavelength and same intensity" as coherent. Identical is not coherent. Shared origin is.
Can you answer these Coherent Sources MCQs?
Select an option to see the explanation. Wrong answers show why your choice was tempting — and name the exact trap it exploits.
MCQ 1Easy RecallPractice
Two sources are coherent if the phase difference between the waves they emit, measured at a given point, is
Show answer and why every option is right or wrong
Answer: D. D is correct. NCERT Class 12 Physics Chapter 10, page 264, defines coherent sources by a phase difference that remains constant in time; its value may be anything, including non-zero.
Why A is wrong: A is wrong because it states the special case of zero phase difference as if it were the definition. Two slits at different path distances from a screen point have a non-zero but steady phase difference, and the interference there is perfectly sustained.
Why B is wrong: B is wrong because random variation is exactly what destroys sustained interference. Slowing the variation only means the pattern drifts slowly; it still does not stay put.
Why C is wrong: C is wrong because π is simply another particular fixed value, giving a dark point rather than no interference. Singling it out mistakes one outcome for the defining condition.
MCQ 2Concept TrapPractice
Light from two separate but identical sodium lamps falls on a screen. The observed illumination is uniform, with no fringes. The reason is that
Show answer and why every option is right or wrong
Answer: B. B is correct. Independent sources emit in short random-phase bursts, so the interference pattern reshuffles far faster than any detector responds and the time-averaged result is uniform, consistent with the constancy requirement on page 264 of NCERT Class 12 Physics Chapter 10.
Why A is wrong: A is wrong because the lamps are stated to be identical, so the wavelengths match. Blaming wavelength dodges the actual failure, which is phase, not colour.
Why C is wrong: C is wrong because sodium light interferes readily when a single sodium lamp feeds two slits. The limitation lies in using two independent lamps, not in the light itself.
Why D is wrong: D is wrong because unequal intensities only reduce fringe contrast; the fringes would still appear, merely with brighter minima. Contrast and existence are different questions.
MCQ 3Easy RecallPractice
In a double-slit arrangement, the two slits are illuminated by a single source placed behind them because
Show answer and why every option is right or wrong
Answer: C. C is correct. Feeding both slits from one wavefront means any random phase change in the parent source occurs at both slits together, leaving their difference unchanged — the constancy condition of NCERT Class 12 Physics Chapter 10, page 264.
Why A is wrong: A is wrong because a single source divided between two slits delivers less light to each slit, not more. The arrangement is chosen for phase discipline, not brightness.
Why B is wrong: B is wrong because diffraction at each slit still occurs and is in fact needed to spread the light so the two beams overlap. The single source does nothing to suppress it.
Why D is wrong: D is wrong because two lamps of the same type emit the same wavelength. Their problem is independent random phase, not a colour mismatch.
MCQ 4Direct ApplicationPractice
At a point on the screen in a double-slit experiment, the waves from the two slits arrive with a phase difference of 1.4 rad, unchanging in time. At this point
Show answer and why every option is right or wrong
Answer: C. C is correct. Coherence requires only that the phase difference be constant, which it is; a steady intermediate phase difference gives a steady intermediate intensity. See the definition on page 264 of NCERT Class 12 Physics Chapter 10.
Why A is wrong: A is wrong because it reads the definition as requiring zero phase difference. Every point on a fringe pattern away from a maximum has a non-zero phase difference and is still part of a stable pattern.
Why B is wrong: B is wrong because it invents an extra condition. Multiples of π mark the bright and dark points; they are not a requirement for the pattern to hold still.
Why D is wrong: D is wrong because rapid fluctuation is the signature of independent sources with drifting phase. Here the phase difference is stated to be unchanging, so nothing fluctuates.
MCQ 5Easy RecallPractice
For a clearly visible sustained interference pattern, the amplitudes of the two interfering waves should be nearly equal. This condition affects
Show answer and why every option is right or wrong
Answer: A. A is correct. Equal amplitudes make the minima approach zero intensity, maximising contrast; coherence and fringe position are unaffected, per the conditions discussed alongside the definition on page 264 of NCERT Class 12 Physics Chapter 10.
Why B is wrong: B is wrong because coherence is a phase property. Two waves of very different amplitude drawn from one wavefront remain fully coherent.
Why C is wrong: C is wrong because the position of the pattern is set by the phase relationship between the sources, not by how their amplitudes compare. Unequal amplitudes leave the fringes exactly where they were.
Why D is wrong: D is wrong because fringe spacing is fixed by the geometry and the wavelength. Changing the relative amplitudes does not move the fringes closer or farther apart.
MCQ 6Concept TrapPractice
A device shifts the phase of the light passing through one slit of a double-slit setup by a fixed amount, the same at every instant. The effect on the fringe pattern is that it
Show answer and why every option is right or wrong
Answer: D. D is correct. A fixed added phase keeps the phase difference constant in time, so the sources remain coherent by the page-264 definition in NCERT Class 12 Physics Chapter 10; only the location of zero path-plus-phase difference moves.
Why A is wrong: A is wrong because full reversal happens only for the particular offset of π. The question specifies an unstated fixed amount, so reversal is one special case, not the general result.
Why B is wrong: B is wrong because it treats any non-zero phase difference as a loss of coherence. What matters is that the difference does not change with time, and here it does not.
Why C is wrong: C is wrong because uniform illumination results from a phase difference that varies randomly in time. A fixed offset produces no such averaging.
MCQ 7Direct ApplicationPractice
An ordinary light source emits wave trains lasting about 1 × 10⁻¹⁰ s, each with a random starting phase. Two such independent sources illuminate a screen. The number of times per second the interference pattern is rebuilt with a new phase relationship is of the order of
Show answer and why every option is right or wrong
Answer: A. A is correct. One new phase relationship per wave train of 1 × 10⁻¹⁰ s gives 1/(1 × 10⁻¹⁰ s) = 1 × 10¹⁰ per second — far beyond eye or detector response, which is why the averaged result is uniform, as page 264 of NCERT Class 12 Physics Chapter 10 requires of non-coherent sources.
Why B is wrong: B is wrong because it is far below the reciprocal of 1 × 10⁻¹⁰ s. A rate this low would let the eye follow the changing pattern, contradicting the uniform illumination observed.
Why C is wrong: C is wrong because 1 × 10⁸ per second is the reciprocal of 10⁻⁸ s, the natural lifetime of an excited atom. That is a different quantity from the coherence time, which is the interval over which the phase stays fixed and which NCERT gives as of the order of 10⁻¹⁰ s.
Why D is wrong: D is wrong because it repeats the duration of one wave train instead of inverting it. A rate is the reciprocal of a time interval, not the interval itself.
MCQ 8Direct ApplicationPractice
Which one of the following pairs can act as coherent sources?
Show answer and why every option is right or wrong
Answer: B. B is correct. Both virtual images derive from one original source, so any phase change in that source appears identically in both and their phase difference stays constant — the requirement stated on page 264 of NCERT Class 12 Physics Chapter 10.
Why A is wrong: A is wrong because two lasers, however well matched in wavelength, still have independent and drifting phases. Simultaneous switching sets no lasting relationship between them.
Why C is wrong: C is wrong because a shared power supply controls the electrical input, not the optical phase of individual atomic emissions. Each lamp still emits random-phase wave trains.
Why D is wrong: D is wrong because matched intensity governs fringe contrast, not phase constancy. Two independent lamps remain incoherent no matter how carefully their brightness is balanced.
Free NEET study resources
Get a structured 30-day Mechanics plan and a complete formula booklet — delivered to your inbox instantly.
How do you solve a Coherent Sources question? A worked example
- 1
Given.
• Original setup: one source slit S feeding both S₁ and S₂.• New setup: two independent lamps, one per slit, same wavelength.• Wave-train duration per lamp: τ = 1.0 × 10⁻¹⁰ s.
- 2
Required.
The appearance of the screen in the new setup, and the survival time of any instantaneous pattern.
- 3
Concept.
Sustained interference requires the phase difference between the two arriving waves to be constant in time (NCERT Class 12 Physics Chapter 10, page 264). Equal wavelength is a separate requirement and does not supply this constancy.
4. Relation. Phase difference at a screen point: Δφ = (2π/λ)·(path difference) + (φ₂ − φ₁), where φ₁ and φ₂ are the emission phases of the two sources. Sustained interference needs (φ₂ − φ₁) to hold fixed. - 5
Substitution.
Original setup: S₁ and S₂ are two windows on one wavefront from S, so φ₂ − φ₁ = 0 always — fixed. New setup: φ₁ and φ₂ belong to unrelated lamps, each resetting to a random value once per wave train, so φ₂ − φ₁ is a fresh random number every 1.0 × 10⁻¹⁰ s.
- 6
Calculation.
The pattern survives for one wave-train duration, τ = 1.0 × 10⁻¹⁰ s, and is rebuilt at a rate 1/τ = 1/(1.0 × 10⁻¹⁰ s) = 1.0 × 10¹⁰ per second. The factor 2π in the phase relation is a mathematical constant and the "two" in "two sources" is a counting integer; neither limits the significant figures, so the two-significant-figure input τ = 1.0 × 10⁻¹⁰ s sets the two-significant-figure answer.
- 7
Final answer.
The screen shows uniform illumination with no fringes. An instantaneous pattern exists but survives only about 1.0 × 10⁻¹⁰ s, reshuffling about 1.0 × 10¹⁰ times per second, so every detector records the time average — the sum of the two separate intensities, with the interference term averaged away.
- 8
Common trap.
Answering "no interference occurs." Interference occurs at every instant; what is absent is sustained interference. A question asking whether the waves interfere and a question asking whether fringes are seen have different answers here, and options are routinely written to exploit the gap.
- 9
Similar NEET-style question.
A double-slit pattern is observed with a single source. A thin device is inserted behind one slit that advances the phase of the light through it by a fixed 0.60 rad at all times. State, with reason, whether fringes are still seen and whether the sources are still coherent. *(Answer: yes to both — the added phase is constant, so the phase difference remains constant and the pattern merely shifts sideways.)*
What to remember before solving Coherent Sources questions
More in Optics: 9 exam traps and mistakes · 11 formulas · 7 question patterns from its other lessons.
Coherent Sources questions from past NEET papers
No question in our NEET 2020–2025 set targets this topic directly.
Sources
NCERT refs: Class 12 Physics Chapter 10, p.264
Page numbers are the ones printed in the current NCERT textbook (2023 rationalised edition), unless marked pre-2023. The books are free at ncert.nic.in.
Test yourself on this topic with real past-paper questions:
Practice this topic →