Question

A prism of refractive index $\sqrt{\frac{3}{2}}$ and refracting angle is $45^{\circ }$ is placed in air. One of the two refracting surfaces of the prism is silvered and a ray of monochromatic light enters the prism from the other face at an angle $\theta$ . If the ray retraces its path, then what is the value of $\theta$ (in degree)?

Answer 1

Answer: 60

The monochromatic ray of light will retrace its path if it strikes the mirror perpendicularly.

Using Snell's law of refraction,
$1\times sin\theta =\mu \times sin45^{\circ }$
$\Rightarrow sin\theta =\sqrt{\frac{3}{2}}\times sin45^{\circ }$
$sin\theta =\sqrt{\frac{3}{2}}\times \frac{1}{\sqrt{2}}=\frac{\sqrt{3}}{2}$
$\Rightarrow \theta =60^{\circ }$