Question

The maximum intensity of fringes in Young's experiment is I. If one of the slit is closed, then the intensity at that place becomes I_o. Which of the following relation is true ?

• A. I = I_o
• B. I = 2I_o
• C. I = 4I_o
• D. There is no relation between I and I_o

Answer 1

Answer: (C)

I = 4I_o

Answer 2

Suppose slit width’s are equal, so they produces waves of equal intensity say $I^{'}.$ Resultant intensity at any point $I_{R} = 4I^{'}\cos^{2}\varphi$ where $\varphi$ is the phase difference between the waves at the point of observation.

For maximum intensity $\varphi = 0^{o} \Rightarrow {I'}_{\max}$ …(i)

If one of slit is closed, Resultant intensity at the same point will be $I^{'}$only i.e. $I^{'} = I_{O}$ …(ii)

Comparing equation (i) and (ii) we get $I = 4I_{O}$