Consider following statements for refraction of light through prism, when angle of deviation is minimum.
A. The refracted ray inside prism becomes parallel to the base.
B. Larger angle prisms provide smaller angle of minimum deviation.
C. Angle of incidence and angle of emergence becomes equal.
D. There are always two sets of angle of incidence for which deviation will be same except at minimum deviation setting.
E. Angle of refraction becomes double of prism angle.
Choose the correct answer from the options given below :

Solution

Physics sir · 3 steps

At minimum deviation the path is symmetric: the ray goes in and comes out the same way, r = A/2.

1. Symmetric path. At minimum deviation, i = e and r₁ = r₂ = r. Since r₁ + r₂ = A, each angle of refraction is r = A/2. The ray inside then makes equal angles with both faces, so it runs parallel to the base.

   μ = sin((A+δₘ)/2)/sin(A/2)

2. Effect of prism angle. For a fixed μ, this relation gives δₘ = 2 sin⁻¹(μ sin A/2) - A, which increases as A increases. A larger-angle prism bends light more, not less.

   Statement	True or false	Reason
   A	True	Symmetric path, so the ray inside is parallel to the base
   B	False	δₘ grows with A
   C	True	i = e is the condition for minimum deviation
   D	True	The ray path is reversible, so swapping i and e gives the same δ
   E	False	r = A/2, which is half the prism angle, not double

3. So. The correct statements are A, C and D, which is option (d).

The idea to keep. Minimum deviation means a symmetric path: i = e, r = A/2, ray parallel to the base. At any other deviation, swapping i and e gives the same deviation.

Answer from the NTA final answer key. Solution by PrepWiser.