Question

A ray of light from a liquid $(\mu =\sqrt{3})$ is incident on a system of two right angled prism of refractive indices $\sqrt{3}and\sqrt{2}$ as shown in the figure. The light suffers zero net deviation when it emerges into air from surface CD. If the angle of incidence (in degrees) is $5n$. Find n ?

Answer 1

First, we apply the law of refraction for the interface AC,
The incident angle will be $90-i$

$\sqrt{3}sin(90-i)=\sqrt{2}sinr$

$\sqrt{3}cosi=\sqrt{2}sinr$

Now, for the interface CD,

$\sqrt{2}sin(90-r)=sini$

Thus, $\sqrt{2}cosr=sini$

We have two equations in i and r, squaring and adding these 2,

we get,
$2{cos}^{2}i+1=2$

This gives, $cosi=\frac{1}{\sqrt{2}}$

Thus, $i=45$