Question

The refractive index of glass is $1.5$. From a point P inside a glass slab, draw three rays PA, PB and PC incident on the glass-air surface making angles of incidence ${30}^{\circ }$, ${42}^{\circ }$ and ${60}^{\circ }$ respectively.
(a) In the diagram show the approximate direction of these rays as they emerge out of the slab.
(b) What is the angle of refraction for the ray PB.

Hint: $\sin \left({42}^{\circ }\right)=2/3$

Answer 1

First, we need to find critical angle. From the formula of critical angle,
$\sin c=\frac{1}{n}$
$\sin c=\frac{2}{3}$
$\sin c={42}^{\circ }$
$c={42}^{\circ }$

(a)
When angle of incidence is:

• Smaller than ${42}^{\circ }$, it refracts (PA)
• Equal to ${42}^{\circ }$, it grazes the surface (PB)
• Greater than ${42}^{\circ }$, it undergoes total internal reflection (PC)

(b)
As we saw before, for the ray PB, angle of incidence is equal to critical angle. So, angle of refraction for PB is ${90}^{\circ }$.