Question

For the sustained interference of light, the necessary condition is that the two sources should:
A. Have constant phase difference
B. Be narrow
C. Be close to each other
D. Of the same amplitude

Answer 1

Hint: you can start by briefly explaining interference. Then move on to explain what sustained interference means and also mention that for sustained interference the intensity at any time should not change. Then write the equation for intensity at any point, i.e. $I = A_1^2 + A_2^2 + 2{A_1}{A_2}\cos \phi $ and use it to explain how constant phase difference is important for sustained interference.

Complete answer:
We know that the interference pattern is made up of constructive (produces maximum intensity) and destructive interference (produces minimum interference). For sustained interference, the intensity at any point should not change with time.
We also know that the resultant intensity \[I\] at any point is
$I = A_1^2 + A_2^2 + 2{A_1}{A_2}\cos \phi $
Here, ${A_1} = $ The amplitude of the first wave
${A_2} = $ The amplitude of the second wave
$\cos \phi = $ The phase difference between the two waves
Thus, as the amplitude of the two waves remains constant, to obtain a sustained interference of light the two sources of light must have a constant phase difference.

So, the correct answer is “Option A”.

Additional Information:
In physics, interference is a very important phenomenon. Interference involves the superimposition of two waves which form a resultant with amplitude more, less, or the same as the two waves involved. For interference, it is very important that the two waves either come from the same source or have the same or nearly the same frequency.

Note:
As we discussed earlier that the two waves should have a constant phase difference between them. In labs we do not use waves from two different sources to demonstrate interference, normally we use sodium lamps as a single light source for the two waves. If we do not use waves from the same source then the interference pattern will not be proper.