Question

A prism ABC of angle ${30}^o$ has its face AC silvered. A ray of light incident at an angle of ${45}^o$ at the face AB retraces its path after refraction at face AB and reflection at face AC. The refractive index of the material of the prism is :

• A. $1.5$
• B. $\frac{3}{\sqrt{2}}$
• C. $\sqrt{2}$
• D. $\frac{4}{3}$

Answer 1

The correct option is C $\sqrt{2}$

At the mirrored surface, light must fall normal to the surface to retrace its path.

Using geometry

$(90°-r_1)+90°+30°=180°\therefore r_1=30°$

Now using Snell's law at refraction

$1\times \sin 45°=\mu \times \sin r_1\therefore \mu =\frac{1}{\sqrt{2}}\times 2=\sqrt{2}$