Question

A ray OP of monochromatic light is incident on the face AB of prism ABCD near vertex B at an incident angle of 600. If the refractive index of the material of the prism is√3, which of the following is (are) correct? 

(a) The ray gets totally internally reflected at face CD 

(b) The ray comes out through face AD 

(c) The angle between the incident ray and the emergent ray is 90º

(d) The angle between the incident ray and the emergent ray is 120º 

Answer 1

Correct options are (a), (b) and (c).

Explanation :-

 √3 = sin 60º/ sin r 

so r=30º

θ_c = sin^-1(1/√3) 

sin θ_c = 1/√3 = 0.577 

At point Q, angle of incidence inside the prism is i = 45º 

Since sin i= 1/√2 is greater than sin θ_c = 1/√2 , Ray gets totally internally reϐlected at face CD. Path of ray of light after point Q is shown in figure

From the figure, we can see that angle between incident ray OP and emergent ray RS is 90º therefore, correct options are (a), (b) and (c).