# A ray of light is incident on side of a right angled prism normally. It then falls on the hypotenuse of the prism and gets reflected back as shown. If $\theta=45^{\circ}$ then the refractive index of the material of prism is

$(a)\;1 \\ (b)\;< \sqrt 2 \\ (c)\;=\sqrt 2 \\ (d)\; > \sqrt 2$

## 1 Answer

At the glass air interface on the hypotenuse of the prism reflection takes place, $\theta$ must be greater than the critical angle
$\theta > \theta_c$
$\sin \theta < \sin \theta_c$
$\large\frac{1}{\sqrt 2 } > \frac{1}{\mu g}$
$\mu g > \sqrt 2$
Hence d is the correct answer.
answered Jan 16, 2014 by

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