Question

A light source $\text{S}$ (point source) is placed at the centre of a glass sphere of radius $R$ and refractive index $\mu$. The maximum angle $\theta$ with the $x-$axis (as shown in the figure) an incident light ray can make without suffering total internal reflection is

• A. ${\cos }^{-1}(\frac{1}{\mu })$
• B. ${\sin }^{-1}(\frac{1}{\mu })$
• C. ${\tan }^{-1}(\frac{1}{\mu })$
• D. there will never be total internal reflection.

Answer 1

The correct option is D there will never be total internal reflection.


Within a medium, a light ray travels in straight line.

So, we can say that, ray goes undeviated when it hits the curved surface along the radial direction.

Thus, the angle of incidence,

$i=0^{\circ }.........\left(1\right)$

Also, for glass-air interface,

${\theta }_c={\sin }^{-1}\left(\frac{1}{\mu }\right)>0^{\circ }......\left(2\right)$

From eqs. $\left(1\right)$ and $\left(2\right)$ we can conclude that, ${\theta }_c>i$

Thus, there will never be a total internal reflection as ray goes undeviated when it hits the curved interface radially.

Hence, option (d) is the correct alternative.

Why this question? Note:- A point source produces spherical wavefronts, a perpendicular drawn to the surface of the wavefront at any point is known as ' wavenormal '. The direction in which the light travels is called as 'Ray'. A wave normal is same as a ray of light.