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

Answer: 2

For path difference $\lambda$, phase difference $=2\pi rad$
For path difference $\frac{\lambda }{4}$, phase difference $=\frac{\pi }{2}rad$
As $K=4I_0.$
So, intensity at given point where path difference is $\frac{\lambda }{4}$
$K^{\prime }=4I_0{\cos }^2\left(\frac{\pi }{4}\right)=2I_0=\frac{K}{2}$