Question

A ray of light suffers a minimum deviation when incident on an equilateral prism of refractive index $\sqrt{2}$. The angle of incidence is :

• A. ${30}^o$
• B. ${45}^o$
• C. ${60}^o$
• D. ${50}^o$

Answer 1

The correct option is B ${45}^o$

Given : Refractive index of air, $n_1=1$ Refractive index of prism, $n_2=\sqrt{2}$

Angle of prism, $A=r_1+r_2$

As ray of light suffers minimum deviation, thus $r_1=r_2=r$

$⟹$ $A=2r$

$\therefore$ $r=\frac{A}{2}=\frac{{60}^o}{2}={30}^o$

where $A={60}^o$ (equilateral prism)

Using Snell's law, $n_1\sin i=n_2\sin r$

$\therefore$ $1\times \sin i=\sqrt{2}\times 0.5$

We get: $\sin i=\frac{1}{\sqrt{2}}$ $⟹i={45}^o$