Question

A circular beam of light (diameter d) fells on a plane surface of a liquid. The angle of incident is ${45}^o$ and refractive index of the liquid is $\mu$. The diameter of the refracted beam is

Answer 1

$d=PQ\cos 60°$

$\Rightarrow d=PQ\cos r$

$\Rightarrow \frac{d}{d^1}=\frac{\cos 60°}{\cos r}$

$\sin r=\frac{\sin i}{\mu }=\frac{1}{v_3}$

$\Rightarrow l^{\prime }=2d\cos r=2\left(2\right)\frac{\sqrt{2}}{\sqrt{3}}$

$=\frac{4\sqrt{2}}{\sqrt{3}}$

$=4\sqrt{\frac{2}{3}}$

$=3.26cm$

Hence, the answer is $3.26cm.$