Question

Calculate the angle of incidence on the face of a prism of reflecting angle ${60}^o$ and of refractive index $1.5,$ for which the emergent ray just grazes the other face.

Answer 1

Since the refraction angle $\left(r_2\right)$ of the emergent ray will be equal to the critical angle ${\theta }_c$.

The critical angle is given as,

$\sin {\theta }_c=\frac{1}{\mu }$

$\sin {\theta }_c=\frac{1}{1.5}$

${\theta }_c={41.81}^{\circ }$

The refracted angle is given as,

$r_1=60-41.81$

$r_1=18.19$

The incidence angle is given as,

$\frac{\sin i}{\sin r_1}=\mu$

$\frac{\sin i}{\sin {18.19}^{\circ }}=1.5$

$i={27.92}^{\circ }$

Thus, the angle of incidence is ${27.92}^{\circ }$.