Question

The maximum intensity of fringes in Young's experiment is l. If one of the slits is closed , then intensity at that place becomes $I_0$. then relation between I and $I_0$ is

• A. $I=I_0$
• B. $I=2I_0$
• C. $I=4I_0$
• D. there is no relation between $I$ and $I_0$

Answer 1

The correct option is C $I=4I_0$

Suppose slit width's are equal so they produces waves of equal intensity say $I^{\prime }$, Resultant intensity at any point $I_R=4I^{\prime }{\cos }^2\varphi$ where $\varphi$ is the phase difference between the waves at the point of observation.
For maximum intensity $\varphi =0^o\Rightarrow I_{max}=4I^{\prime }=I......\left(I\right)$
If one of slit is closed. Resultant intensity at the same point will be $I^{\prime }$ only i.e., $I^{\prime }=I_0..\left(ii\right)$
Comparing equation (i) and (ii) we get
$I=4I_0$