Question

A prism of refractive index $\sqrt{2}$ has a refracting angle of ${60}^o.$ At what angle a ray must be incident on it, so that it suffers a minimum deviation.

• A. ${45}^o$
• B. ${60}^o$
• C. ${90}^o$
• D. ${180}^o$

Answer 1

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

The reaction for refractive index of prism is
$\mu =\frac{\sin i}{\sin r}...\left(i\right)$
The condition for minimum deviation is
$r=\frac{A}{2}=\frac{{60}^o}{2}={30}^o$
Putting the given value of $\mu =\sqrt{2}$ and $r={30}^o$ the Eq (i) we get,
$\sqrt{2}=\frac{\sin i}{\sin {30}^o}$
$\sin i=\sqrt{2}\times \frac{1}{2}=\frac{1}{\sqrt{2}}$
$\sin i=\sin {45}^o$
$i={45}^o$