Question

In Young's double-slit experiment, the intensity of light at a point on the screen, where the path difference is $\lambda$, is $I$. The intensity of light at a point where the path difference becomes $\frac{\lambda }{3}$ is :

• A. $\frac{I}{4}$
• B. $\frac{I}{3}$
• C. $\frac{I}{2}$
• D. $I$

Answer 1

The correct option is A $\frac{I}{4}$

We know that :
$I=4I_o^2{\cos }^2\frac{\Delta \varphi }{2}$

In the first case,
$\Delta x=\lambda \Rightarrow \Delta \varphi =\frac{2\pi }{\lambda }\times \lambda =2\pi$
$\therefore I=4I_o^2$

In the second case,
$\Delta x=\frac{\lambda }{3}\Rightarrow \Delta \varphi =\frac{2\pi }{\lambda }\times \frac{\lambda }{3}=\frac{2\pi }{3}$
$\therefore I^{\prime }=4I_o^2{\cos }^2\frac{2\pi }{3}$
or, $I^{\prime }=I_o^2$

$\Rightarrow I^{\prime }=\frac{I}{4}$
Hence, option (a) is correct.