Question

A light ray is incident perpendicular to one face of a ${90}^0$ prism and is totally intemally reflected at the glass-air interface. If the angle of reflection is ${45}^0$, we conclude that the refractive index $n$:

• A. $n<\frac{1}{\sqrt{2}}$
• B. $n>\sqrt{2}$
• C. $n>\frac{1}{\sqrt{2}}$
• D. $n<\sqrt{2}$

Answer 1

The correct option is B $n>\sqrt{2}$

For grazing emergent ray, $\mu sin{\theta }_c=1⟹sin{\theta }_c=\frac{1}{\mu }$

For total internal reflection, $sin\theta >sin{\theta }_c$

$⟹\frac{1}{\sqrt{2}}>\frac{1}{\mu }$ ($\theta ={45}^o$)

Thus $\mu >\sqrt{2}$