Question

In the Young's double-slit experiment, the intensity of light at a point on the screen where the path difference is $\lambda$ is $K$, ( $\lambda$ being the wave length of light used). The intensity at a point where the path difference is $\frac{\lambda}{4}$, will be $\frac{K}{n}$. Find $n$

Answer 1

For path difference $\lambda$, phase difference $=2 \pi rad$
For path difference $\frac{\lambda}{4}$, phase difference $=\frac{\pi}{2} rad$
As $K=4 I_{0} .$
So, intensity at given point where path difference is $\frac{\lambda}{4}$
$K'=4 I_{0} \cos ^{2}\left(\frac{\pi}{4}\right)=2 I_{0}=\frac{K}{2}$