A ray of light is incident on a prism at an angle of 45o and passes symmetrically as shown in the figure. Calculate:

(a) the angle of minimum deviation,
(b) the refractive index of the material of the prism, and
(c) the angle of refraction at the point P.

(a) When rays passes symmetrically ,then rays is going to through minimum deviation.
Minimum deviation δ = 2i−A
An equilateral prism so, A is prism angle A = 60°
δ = 2(45°) − 60° = 30°
For minimum angle the angle of refraction should be half of prism angle.
So r = A/2 = 30°
(b) Now using the snell's law,
nair sini = n_glass sin r
1 × sin45 = n_glass sin30
n_glass = 0.50 / 0.707
n_glass = 0.707
(c) For minimum angle the angle of refraction should be half of prism angle.
So r = A/2 = 30°