When light in air strikes the flat surface of a certain glass at 31.2° with the normal,the reflected ray is 100 percent polarized.What is the critical angle for the air-glass interface of this glass?
A)52.7°
B)58.8°
C)21.4°
D)37.3°
E)68.6°

Question

Quizplus · Accepted Answer

For total reflection, the angle of incidence must be greater than or equal to the critical angle.

Since the reflected ray is 100 percent polarized, we know that the angle of incidence (i) is equal to the Brewster angle (B):

i = B = 31.2°

Using Snell's Law:

n1sin(i) = n2sin(r)

where n1 is the refractive index of air (approximately 1.00) and n2 is the refractive index of the glass.

Rearranging, we get:

sin(r) = n1/n2 * sin(i)

Taking the sine inverse of both sides:

r = sin^-1(n1/n2 * sin(i))

At the critical angle, r = 90°, so:

sin^-1(n1/n2 * sin(i)) = 90°

sin(i) = n2/n1 * sin(90°) = n2

Solving for n2:

n2 = sin(i) = sin(31.2°) ≈ 0.52

Now we can use Snell's Law again to find the critical angle:

n1sin(crit) = n2sin(90°)

sin(crit) = n2/n1 * sin(90°) = n2

sin(crit) ≈ 0.52

crit ≈ 37.3°

Therefore, the correct answer is D) 37.3°.

When Light in Air Strikes the Flat Surface of a Certain