Question

The necessary condition for an interference by two sources of light is that:
(A) Two light sources must have the same wavelength
(B) Two point-sources should have the same amplitude and same wavelength
(C) Two sources should have the same wavelength, nearly the same amplitude and have constant phase angle difference
(D) The two point-sources should have a randomly varying phase difference

Answer 1

To reach at the answer, continue with the basics about what interference is and the basic need of the interference is nothing but the condition of the two sources to be coherent. Any of the correct options should have the major condition of the sources being coherent.

Complete step by step solution:
As explained in the hint section of the solution to the asked question, we need to look out for the option which has at least the condition of the sources of light waves to be coherent. To do that, we need to know what coherent sources of light waves are. But before that, let us first explain what interference of light is and how it is produced.
Interference is the phenomenon in which two light waves are superimposed to form a resultant wave of amplitude greater or lower than the amplitudes of the either waves. Interference usually refers to the interaction of waves that are correlated or coherent with each other, either because they come from the same source or because they have nearly the same frequency.
Now that we have explained what interference of light waves is, we can observe that we used the term coherent with each other. Two waves can be coherent with each other if their sources are coherent meaning that the two sources have nearly the same frequency and thus, the phase difference between the waves of these two sources is always constant, i.e. time does not affect the phase angle difference between these two sources or the light produced by the two coherent sources.
As we can see in the given options, only option (C) gives this condition that the two sources should have the same wavelength, nearly the same amplitude and a constant phase angle difference.

So, option (C) is the correct answer.

Note: Many students may argue that option (B) is also correct since these conditions are also a must for interference of waves. But these conditions are not sufficient, if the sources are not coherent and wavelength and amplitude meet the condition, the interference may not happen throughout the study.