Ray optics

Question

An equilateral prism ABC is placed in air with its base side BC lying horizontally along x-axis. A light ray $\sqrt{3}z+x=10$ is incident at a point P on face AB of the prism.

The value of $\mu $ of prism for which the ray grazes the face AC is

Easy

Solution

This ray falls normally on AB ${r}_{1}=0,{r}_{2}=A=C={60}^{0}$

$\mu =\frac{1}{\mathrm{sin}{60}^{0}}=\frac{2}{\sqrt{3}}$

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