Question

A ray of light strikes a cubical slab as shown in the figure. Then the geometrical path length traveled by the light in the slab will be:

• A. $2\sqrt{3}$
• B. $6$
• C. $\frac{2}{\sqrt{3}}$
• D. $\frac{\sqrt{3}}{2}+\frac{3}{2}$

Answer 1

The correct option is B $6$

At the top surface, $\frac{\sin 60}{\sin r}=\sqrt{\frac{3}{2}}$

$\sin r=\frac{1}{\sqrt{2}}$

$r={45}^{\circ }$

For medium 2,${45}^{\circ }$ is greater than its critical angle.

Therefore it undergoes total internal reflection.

From fig. $AB=BC=CD=2m$

Total optical path $=2+2+2=6m$