57. A ray of light is incident at an angle of incidence, i, on one face of prism of angle A (assumed to be small) and emerges normally from the opposite face. If the refractive index of the prism is μ, the angle of incidence i, is nearly equal to :

57. A ray of light is incident at an angle of incidence, i, on one face of prism of angle A (assumed to be small) and emerges normally from the opposite face. If the refractive index of the prism is μ, the angle of incidence i, is nearly equal to :

(a) \(\mu A\)

(b) \(\mu A^2\)

(c) \(\tfrac{A}{\mu}\)

(d) \(\tfrac{A}{2\mu}\)

Answer :  (a) \(\mu A\)

\(\tfrac{sin i}{sin r} = \mu\)

\(\tfrac{sin i}{sin A} = \mu\)

\(\tfrac{i}{A} = \mu\)