Question

There is a prism with refractive index equal to $\sqrt{2}$ and the refracting angle equal to 30°. One of the refracting surfaces of the prism is polished. A beam of monochromatic light will retrace its path if its angle of incidence over the refracting surface of the prism is

• A. Zero
• B. 30°
• C. 45°
• D. 60°

Answer 1

The correct option is C 45°

To retrace the path, the angle of incidence 'i' on the surface AB should be such that after refraction, the ray PQ strikes perpendicular to the polished surface AC as shown in figure.

According to Snell's law, $\frac{sin\left(i\right)}{sin\left(r\right)}$
$\Rightarrow \mu =\frac{sin\left(i\right)}{sin\left({30}^o\right)}$
$\Rightarrow sin\left(i\right)=\mu sin{30}^o$
$\Rightarrow \text{sin (i)}=\sqrt{2}\times \frac{1}{2}=\frac{1}{\sqrt{2}}$
$\Rightarrow i={45}^o$
Hence, the correct answer is option (c).