Question

A ray of light travelling in a transparent medium of refractive index $\mu$, falls on a surface separating the medium from air at an angle of incidence of 45$^{\circ}$. For which of the following value of $\mu$. the ray can undergo total internal reflection?

• A. $\mu =1.33$
• B. $\mu =1.40$
• C. $\mu =1.50$
• D. $\mu =1.25$

Answer 1

Answer: (C)

$\mu =1.50$

Answer 2

For total internal reflection,
$\sin\, i > \sin\, C$
where
$i =$ angle of incidence
$C =$ critical angle
But , $sin C = \frac{1}{\mu }$
$\therefore \, \, \, \sin\, i > \frac{1}{\mu} \, \, or \, \, \mu > \frac{1}{ \sin \,i }$
$\mu > \frac{1}{ \sin\, 45 ^ \circ }$ $(I = 45^{\circ}$ (Given))
$\mu > \sqrt 2$
Hence, option (c) is correct.