Question 378: Ray Optics

Question

A ray OP of monochromatic light is incident on the face AB of prism ABCD near vertex B at an incident angle of 60$$^\circ$$ (see figure). If the refractive index of the material of the prism is $$\sqrt3$$, which of the following is(are) correct?

Accepted Answer

Consider the refraction at the face AB. Snell's law,
$$\sin i/\sin r = \sin 60^\circ /\sin r = \sqrt 3 $$,
gives $$r = 30^\circ $$.
The geometry in BCQP gives
$$\angle BPQ = 30^\circ  + 90^\circ  = 120^\circ $$
$$\angle CQP = 360^\circ  - (135^\circ  + 60^\circ  + 120^\circ ) = 45^\circ $$.
Thus, the angle of incidence at Q is $${i_1} = 45^\circ $$. The critical angle for prism to air refraction is given by $$\sin {i_c} = 1/\sqrt 3 $$. Since $$\sin {i_1} = 1/\sqrt 2  > 1\sqrt 3 $$, we get $${i_1} > {i_c}$$ i.e., the angle of incidence is greater than the critical angle. Thus, the ray undergoes total internal reflection at Q. The laws of reflection gives $${r_1} = {i_1} = 45^\circ $$. In triangle QRD, $$\angle QRD = 60^\circ $$ and hence the angle of incidence at R is $${i_2} = 30^\circ $$.
Applying Snell's law at face AD, we get
$$\sqrt 3  	imes \sin 30^\circ  = 1 	imes \sin e$$
or, $$\sqrt 3  	imes {1 \over 2} = \sin e$$
$$\sin e = {{\sqrt 3 } \over 2}$$
or, $$e = {\sin ^{ - 1}}\left( {{{\sqrt 3 } \over 2}} ight) = 60^\circ $$
From figure,
The angle between the incident ray and the emergent ray is 90$$^\circ$$.
Hence, option (c) is correct and option (d) is incorrect.
Note : Angle between incident and emergent rays is the same as the angle between the two faces = 90$$^\circ$$.

Answer

The ray gets totally internally reflected at face CD.

Answer

The ray comes out through face AD.

Answer

The angle between the incident ray and the emergent ray is 90$$^\circ$$.

Answer

The angle between the incident ray and the emergent ray is 120$$^\circ$$.

Ray Optics

A ray OP of monochromatic light is incident on the face AB of prism ABCD near vertex B at an incident angle of 60$^\circ (see figure). If the refractive index of the material of the prism is \sqrt3$, which of the following is(are) correct?

Choose the correct answer: