For an isosceles prism of angle and refractive index

PHYSICS · Single correct · CBSE · Physics · Ray Optics and Optical Instruments · Ray Optics and Optical Instruments

Problem

For an isosceles prism of angle

A

and refractive index

\mu

, it is found that the angle of minimum deviation

\delta_m = A

. [Adv. 2017] Which of the following options is/are correct? (1) For the angle of incidence

i_1 = A

, the ray inside the prism is parallel to the base of the prism (2) For this prism, the refractive index

\mu

and the angle of prism

A

are related as

A = \frac{1}{2} \cos^{-1} \left( \frac{\mu}{2} \right)

(3) At minimum deviation, the incident angle

i_1

and the refracting angle

r_1

at the first refracting surface are related by

r_1 = (i_1/2)

(4) For this prism, the emergent ray at the second surface will be tangential to the surface when the angle of incidence at the first surface is

i_1 = \sin^{-1} \left[ \sin A \sqrt{4 \cos^2 \frac{A}{2} - 1 - \cos A} \right]