Question

A large glass slab $(\mu =5/3)$ of thickness 8 cm is placed over a point source of light on a plane surface. It is seen that light emerges out of the top surface of the slab from a circular area of radius R cm. What is the value of R?

Answer 1

Light will appear only from a circular region because rays going out at an angle greater than ${\theta }_c$ will suffer TIR.
$\sin {\theta }_c=\frac{1}{\mu }=\frac{3}{5}$
From figure,
$\sin {\theta }_c$
$=\frac{R}{\sqrt{R^2+8^2}}$

Equating,
$\frac{R}{\sqrt{R^2+8^2}}=\frac{3}{5}$
Solving,
$R=6cm$