Question

A plane-polarized blue light ray is incident on a prism such that there is no reflection from the surface of the prism. The angle of deviation of the emergent ray is 𝛿 = 60° (see Figure-1). The angle of minimum deviation for red light from the same prism is 𝛿min = 30° (see Figure-2). The refractive index of the prism material for blue light is √3. Which of the following statement(s) is(are) correct?

• A. The blue light is polarized in the plane of incidence.
• B. The angle of the prism is 45°
• C. The refractive index of the material of the prism for red light is √2.
• D. The angle of refraction for blue light in air at the exit plane of the prism is 60°.

Answer 1

Answer: (A), (C), (D)

The blue light is polarized in the plane of incidence.

Answer 2

The correct options are (A),(C) and(D).
For no reflection,

$tan\,i=\sqrt3$
$i=60$
$\frac{sin\,i}{sin\,r_1}=\sqrt3, r_1=30^{\circ}$
$\delta=i+e-r_1-r_2=60^{\circ}$
$e=60^{\circ},r_2=30^{\circ}$
$A=60^{\circ}$
For red lights,
$\mu=\frac{sin(\frac{A+\delta_m}{2})}{sin\frac{A}{2}}=\sqrt2$