Question

A light ray is incident at an angle of ${45}^0$ with the normal to a $\sqrt{2}$ cm thick plate ($\mu =2.0$). Find the shift in the path of the light as it emerges out from the plate.

Answer 1

Here, $i={45}^0\Rightarrow \sin r=\frac{\sin i}{\mu }=\frac{1}{2\sqrt{2}}$

$\Rightarrow r={\sin }^{-1}\left(1/2\sqrt{2}\right)={20.7}^0$

Lateral Displacement $=\frac{t\sin (i-r)}{\cos r}$

$=\frac{\sqrt{2}\times \sin ({45}^0-{20.7}^0)}{\cos {20.7}^0}=0.622cm$