Question

The cross section of glass prism has the form of an isosceles triangle . One of equal face is silvered. A ray of light incident normally on other equal face and after being reflected twice, emerges through base of prism along normal. That the angle of prism is :-

Answer 1

The angles of prism are 72°, 72° and 36° respectively.

Explanation:

r1 = 0

r2 = A = 180° - 2θ --- (1)

angle DFE = 180°  - 90° - 2r2

                 = 180°  - 90° - 360° + 4θ

                 = 4θ   - 270°

r3 = 90° - angle DFE

r3 = 360° -  4θ

Angle BFG = 90° - θ = 90°  - r3

r3 = θ

Form equations 91) and (2)

5θ  = 360°

θ  = 72°

and 180° - 2θ = 36°

Thus the angles of prism are 72°, 72° and 36° respectively.