The exit surface of a prism with refractive index n is coated with a material having refractive index $$\frac{n}{2}$$. When this prism is set for minimum angle of deviation, it exactly meets the condition of critical angle. The prism angle is ___ .

Minimum Deviation Condition

$$ r_1 = r_2 = \frac{A}{2} $$
A is the angle of the prism.

Critical Angle Condition at Exit Surface

Using Snell's Law at the exit surface (prism to coating):
$$ n \sin(r_2) = n_{\text{coating}} \sin(90^\circ) $$

Given that $$n_{\text{coating}} = \frac{n}{2}$$ and substituting $$r_2 = \frac{A}{2}$$:
$$ n \sin\left(\frac{A}{2}\right) = \left(\frac{n}{2}\right) \cdot 1 $$

$$ \sin\left(\frac{A}{2}\right) = \frac{1}{2} $$
$$ \frac{A}{2} = 30^\circ $$
$$ A = 60^\circ $$