Question

Two sources of light are said to be coherent, when they give light waves of same:
A. amplitude and phase.
B. wavelength and constant phase difference
C. intensity and wavelength
D. phase and speed

Answer 1

Hint: Two coherent sources come from a single original source, and thus have the same frequency.

Complete step by step solution:
Every source of light is made up of innumerable atoms, which are the ultimate sources of light. When an atom gets energy, its electrons go to some higher orbit or excited state, that lasts only for about s after which the electron jumps back to the lower orbit. During this jump, the atom radiates light (photons). That is, the atom does not emit a continuous infinite train of light waves, but emits wave-pulses at short intervals. These short intervals are different for different atoms. Therefore, the innumerable atoms in the source emit light waves whose phase varies with time in a random way. Evidently, if we take two independent light-sources, then the phases of the waves emitted by then will vary independently of each other, that is, the phase difference between them will not remain steady and the waves will not form a sustained interference pattern.
If two sources are derived from a single original source, then any phase change in the wave emitted by one will simultaneously be accompanied by the same phase-change in the wave emitted by the other. Thus, the phase difference between the waves from the two sources will remain constant. Such sources are called coherent sources. As these sources are from a single original source, their frequency or wavelength will be the same.

Thus, two sources of light are said to be coherent, when they give light waves of same wavelength and constant phase difference.

So, option B is the correct answer.

Note: If the phase difference between two light waves arriving at a point vary with time in a random way, the wave-sources are said to be incoherent. They cannot produce sustained interference.