Question

A ray of light traveling in a transparent medium falls on a surface separating the medium from the air at an angle of incidence of ${45}^{\circ }$. The ray undergoes total internal reflection. If $n$ is the refractive index of the medium with respect to air, select the possible value(s) of $n$ from the following.

• A. $1.3$
• B. $1.4$
• C. $1.5$
• D. $1.6$

Answer 1

Answer: (C), (D)

The correct options are
C $1.5$
D $1.6$

${\theta }_{critical}=si{n}^{-1}\left(\frac{1}{\mu }\right)$

(i) $\mu =1.3$

${\theta }_{critical}=si{n}^{-1}\left(\frac{1}{1.3}\right)\Rightarrow {50.28}^0$

(ii) $\mu =1.4$
${\theta }_{critical}=si{n}^{-1}\left(\frac{1}{1.4}\right)\Rightarrow {45.58}^0$

(iii)$\mu =1.5$
${\theta }_{critical}=si{n}^{-1}\left(\frac{1}{1.5}\right)\Rightarrow {41.8}^0$

(iv)$\mu =1.6$
${\theta }_{critical}=si{n}^{-1}\left(\frac{1}{1.6}\right)\Rightarrow {38.68}^0$

Hence the correct option will be option c and d.