A ray is incident normally on the face of an equilateral prism of refracting angle of 60°. The refractive index of the prism is $\frac{2}{\sqrt{3}}$. The angle of deviation will be:

30°

The correct answer is Option (3) → 30°

Using Snell's law,

$μ\sin r = \sin e$

and, for an equilateral triangle,

$r_1+r_2=A$ $[r_1=0°]$

$⇒r_2=60°$

$∴\frac{2}{\sqrt{3}}\sin 60°=\sin e$

$\frac{2}{\sqrt{3}}×\frac{\sqrt{3}}{2}=\sin e⇒e=90°$

and,

Angle of deviation $(δ)=(i+e)-A$

$=(0+90)-60=30°$