Question

An equilateral prism has an angle of minimum deviation $30^\circ $ . Find total deviation if a ray is incident normally on the surface.

• A. $120^\circ $
• B. $60^\circ $
• C. $90^\circ $
• D. none of these

Answer 1

Answer: (B)

$A=60^\circ $ and $\delta_{m}=30^\circ $
$\mu =\frac{sin \left(\frac{A + \left(\delta\right)_{m}}{2}\right)}{sin ⁡ \frac{A}{2}}$
$\mu =\frac{sin \left(\frac{60 + 30}{2}\right)}{sin ⁡ \frac{60}{2}}$
$\mu =\frac{sin 4 5 ^\circ }{sin ⁡ 3 0 ^\circ }$
$\mu =\frac{\frac{1}{\sqrt{2}}}{\frac{1}{2}}$
$\mu =\sqrt{2}$
Therefore, $\theta_{\text {critical }}=\sin ^{-1}\left(\frac{1}{\mu}\right)$
$\theta _{c r i t i c a l}=45^\circ $
Therefore after $1^{s t}$ incidence light goes straight. At second incidence, total internal reflection takes place, and hence deviation is $\delta=60^\circ $ .