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

$(a)\;1.3 \\ (b)\;1.4 \\ (c)\;1.5 \\ (d)\;1.6$

According to the Snell's law $n_1 \sin \theta_1=n_2 \sin \theta_2$
Given $n_1=n; \sin \theta_1=\sin 45^{\circ}=\large\frac{1}{\sqrt 2}$
$n_2 \geq 1; \theta \geq 90^{\circ}$
$\therefore \sin \theta_2 =\large\frac{n_1}{n_2}$
$\sin \theta_2 =\large\frac{n_1}{1} \bigg( \large\frac{1}{\sqrt 2}\bigg)$
Since for internal reflection $\theta_2 \geq 90^{\circ}$
limiting value of $\sin \theta_2 = \large\frac{n}{\sqrt 2}$$=1$ or $n= \sqrt 2$
Thus ray will undergo total internal reflection if $n \geq \sqrt 2$
Hence b is the correct answer.

edited Jul 23, 2014