Question

A ray PQ is incident normally on the face AB of a triangular prism of refracting angle of ${60}^o$, made of a transparent material of refractive index $\frac{2}{\sqrt{3}}$ as shown in the figure. Trace the path of the ray as it passes through the prism. Calculate the angle of emergence and angle of deviation.

Answer 1

The incident ray is normal to the face AB.
Thus we get $i_1=0^o$ and $r_1=0^o$
Now this ray would refract at the face AC with the incident angle here as $r_2$ and the emergence angel as $e$.
We know that Angle of prism $A$ is given as $r_1+r_2$. Thus we get $r_2={60}^o$
Now Refractive index of the prism is given as $\mu =\frac{sine}{sin{r}_2}$
or
$\frac{2}{\sqrt{3}}=\frac{sine}{\sqrt{3}/2}$
Thus we get $e={90}^o$
And angle of deviation is given as
$\delta =i_1+e-A={30}^0$