Question

A parallel beam of light of wavelength $500\text{nm}$ is incident at an angle ${30}^{\circ }$ with the normal to the slit plane in a Young's double slit experiment. The intensity due to each slit is $I_0$. Point $O$ is equidistant from $S_1$ and $S_2$. The distance between slits is $1\text{mm}$. Choose the correct statement.

• A. The intensity at $O$ is zero.
• B. The intensity at $O$ is $4I_0$.
• C. The intensity at $O$ is $2I_0$.
• D. The intensity at $O$ is $I_0/2$.

Answer 1

The correct option is B The intensity at $O$ is $4I_0$.


Path difference at $O$ is,

$\Delta x=M{S}_1=d\sin \theta$

$\Delta x=M{S}_1={10}^{-3}\times \sin {30}^{\circ }$

$\Rightarrow \Delta x=5\times {10}^{-4}\text{m}$

Now, $\frac{\Delta x}{\lambda }=\frac{5\times {10}^{-4}}{5\times {10}^{-7}}=1000$

$\therefore \Delta x=1000\lambda$

$\therefore {1000}^{th}$ maxima is formed at $O$.

$\therefore$ The intensity at $O$ is $I_{max}=4I_0$

Hence, option $\left(\text{B}\right)$ is correct.