Question

Statement 1: All points on a wavefront vibrate in the same phase and with the same frequency.
Statement 2: two sources are said to be coherent if they produce waves of the same frequency and with a constant phase difference.
(A) Statement 1 is true, statement 2 is true. Statement 2 is the correct explanation of statement 1
(B) Statement 1 is true, statement 2 is true. Statement 2 is not the correct explanation of statement 1
(C) Statement 1 is true and statement 2 is false.
(D) Statement 1 is false and statement 2 is true.

Answer 1

A wavefront is a surface over which a wave has a constant phase. Wavefront came into existence from Huygen’s theory of wave picture of light. Wavefront determines the nature and propagation of a light emanating from the given source.

Complete step by step answer:
Wavefront of a time-varying field in physics is the set of all points where the wave has the same phase and from that wavefront light waves moves equally in all directions. Also, no backward wavefront is possible in accordance with Hygen’s principle because energy cannot be negative. All the points on the wavefront have the same temporary displacement. But they don’t need to be oscillating with the same frequency and constant phase difference. So, from the above discussion it is clear that on a wavefront all points do not vibrate in the same phase and frequency. Hence, the statement 1 is false.Now coming to the second statement we know from the young’s double slit experiment and the theory of interference of light that two sources are said to be coherent if they produce waves of same frequency and with a constant phase difference. So, the second statement is also true.

So, the correct option is (D)

Note: One should always keep in mind that frequency is the characteristic of the source of the light and it does not change with the change in medium or with light undergoing any optical phenomenon. Using the hygen’s principle one can also prove the laws of the reflection and refraction of light.