Question:
Assertion (A): Light added to light can produce darkness.
Reason (R): When two coherent light waves interfere, there is darkness at position of destructive interference.
Assertion (A): Light added to light can produce darkness.
Reason (R): When two coherent light waves interfere, there is darkness at position of destructive interference.
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Interference is redistribution of energy, not destruction of light.
Updated On: Jul 2, 2026
- Both A and R are true and R explains A
- Both A and R are true but R does not explain A
- A is true but R is false
- A is false and R is false
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The Correct Option is A
Solution and Explanation
Concept:
One of the most important consequences of the wave nature of light is the phenomenon of interference.
When two coherent light waves overlap in space, the resultant intensity at a point depends upon the phase difference between the waves.
The principle of superposition states that the resultant displacement at any point is equal to the algebraic sum of the individual displacements produced by the two waves.
Depending on the phase relationship, interference may be constructive or destructive.
Assertion Analysis:
The assertion states that light added to light can produce darkness.
At first sight this statement may appear contradictory because we normally expect the addition of two light beams to produce brighter illumination.
However, according to wave optics, when two coherent light waves meet with a phase difference of
[
\pi
]
(or an odd multiple of (\pi)), their amplitudes cancel each other.
If the amplitudes of the two interfering waves are equal, the resultant amplitude becomes zero.
Since intensity is proportional to the square of amplitude,
[
I \propto A^2,
]
the intensity at that point also becomes zero.
As a result, a dark fringe is produced even though light from two sources is present.
Thus, light added to light can indeed produce darkness.
Therefore, the Assertion is TRUE.
Reason Analysis:
The reason states that when two coherent light waves interfere, darkness is produced at positions of destructive interference.
For destructive interference, the path difference between the two waves is
[
(2n+1)\frac{\lambda}{2},
]
where (n=0,1,2,\ldots)
or equivalently, the phase difference is
[
(2n+1)\pi.
]
Under this condition, the crest of one wave coincides with the trough of the other wave, leading to cancellation of amplitudes.
Consequently, the resultant intensity becomes minimum and dark fringes are formed.
Therefore, the Reason is also TRUE.
Relationship Between Assertion and Reason:
The phenomenon described in the Reason is exactly the physical explanation of the Assertion.
Darkness is obtained because of destructive interference between coherent light waves.
Thus the Reason correctly explains why light added to light can produce darkness.
Final Answer:
[
(A)
]
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