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 ${\delta }_m=30^{\circ }$
$\mu =\frac{sin\left(\frac{A+{\left(\delta \right)}_m}{2}\right)}{sin\frac{A}{2}}$
$\mu =\frac{sin\left(\frac{60+30}{2}\right)}{sin\frac{60}{2}}$
$\mu =\frac{sin45^{\circ }}{sin30^{\circ }}$
$\mu =\frac{\frac{1}{\sqrt{2}}}{\frac{1}{2}}$
$\mu =\sqrt{2}$
Therefore, ${\theta }_{\text{critical }}={\sin }^{-1}\left(\frac{1}{\mu }\right)$
${\theta }_{critical}=45^{\circ }$
Therefore after $1^{st}$ incidence light goes straight. At second incidence, total internal reflection takes place, and hence deviation is $\delta =60^{\circ }$ .