Question

A ray of light is incident normally on one of the faces of a prism of apex angle ${30}^o$ and refractive index $\sqrt{2}$. The angle of deviation of the ray is

• A. $0^o$
• B. ${12.5}^o$
• C. ${15}^o$
• D. ${22.5}^o$

Answer 1

Answer: (C)

${15}^o$

Using geometry in the figure, we get incident angle at prism face AC $i={30}^o$

Snell's law at P : $\mu$ $sini=1\times sinr$

$\therefore$ $\sqrt{2}\times sin{30}^o=sinr$ $⟹r=si{n}^{-1}(\frac{1}{\sqrt{2}})={45}^o$

Thus deviation of ray: $\delta =r-i={45}^o-{30}^o={15}^o$