Question

A ray of light passes through as equilateral glass prism such that the refracted ray inside the prism is parallel to its base. How is the angle of emergence ${}^{\prime }{i}_2^{\prime }$ related to the angle of incidence ${}^{\prime }{i}_1^{\prime }$

Answer 1

In equilateral triangle all angles are of ${60}^0$

and it is given that refracted ray is parallel to base of triangle

then

$\angle r_1+\angle r_2={60}^0$

and $\angle r_1=\angle r_2={30}^0$

by snell's law

At first surface AB

$\mu =\frac{sin{i}_1}{sin{30}^0}\left(1\right)$

At surface AC
$\frac{1}{\mu }=\frac{sin{30}^0}{sin{i}_2}\left(2\right)$

by solving 1 and 2 we get

$\angle i_1=\angle i_2$