Question

A plain 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 $\delta$ = 60$^{\circ}$ (figure 1). The angle of min. deviation for red light from the same prism is min $\delta_{min}$ = 30$^{\circ}$ (figure 2). If the refractive index of prism material for blue light is √3, then which of the following options is correct?

PPBL = Plane Polarized Blue Light PPRL = Plane Polarized Red Light

• A. Angle r for blue light in air at the exit plane of the prism is 60$^{\circ}$
• B. The angle of the prism is 45$^{\circ}$
• C. Blue light is polarized in the plane of incidence
• D. The refractive index of the material of the prism for red light is √2

Answer 1

Answer: (B), (C), (D)

The angle of the prism is 45$^{\circ}$

Answer 2

The correct options are: (B),(C) and (D).
For blue light,
$\mu=tan\,i_p$
$\sqrt3=tan\,i_p$
$i_p=60^{\circ}$
$\delta=i+e-A$
$60=60+e-A$
$e=A$
$sin\,60^{\circ}=\sqrt3\,sin\,r_1$
$\frac{\sqrt3}{2}=\sqrt3\,sin\,r_1$
$r_1=30^{\circ}$
$r_2=A-30^{\circ}$
$\sqrt3sin\,(A-30^{\circ})=sin\,A$
$\frac{3}{2}sinA-\frac{\sqrt3}{2}cosA=sinA$
$\frac{-\sqrt3}{2}cosA=-\frac{sinA}{2}$
$tanA=\sqrt3$
$A=e=60^{\circ}$
For red light, $\frac{sin(\frac{A+\delta_{min}}{2})}{sin\frac{A}{2}}=n_R$
$\frac{sin\frac{90}{2}}{sin\,30}=n_R$
$n=\sqrt2$