If light reflected from a transparent substance at an angle of 58.0º is completely plane polarized,light incident at an angle of 32.0º is refracted at an angle of
A)32.0º
B)58.0º
C)19.3º
D)90.0º
E)70.7º

Question

Quizplus · Accepted Answer

When light is incident on a transparent substance, it undergoes both reflection and refraction. At a certain angle of incidence, called the Brewster's angle, the reflected light becomes completely plane polarized, which means that the electric field vector of the reflected light is perpendicular to the plane of incidence.

We can use Snell's law to determine the angle of refraction:

n1*sin(theta1) = n2*sin(theta2)

where n1 is the refractive index of the medium the light is coming from (usually air), theta1 is the angle of incidence, n2 is the refractive index of the transparent substance, and theta2 is the angle of refraction.

At the Brewster's angle, there is no reflected light perpendicular to the plane of incidence, so we know that theta1 + theta2 = 90 degrees. Since theta1 = 58.0 degrees, we can find theta2:

theta2 = 90 degrees - theta1
       = 90 degrees - 58.0 degrees
       = 32.0 degrees

Now we can use Snell's law to find the angle of refraction when the incident angle is 32.0 degrees:

n1*sin(theta1) = n2*sin(theta2)

sin(32.0 degrees) = (n2/n1)*sin(theta2)

We don't know the refractive indices, but we can assume that they are constant for this substance. Therefore, sin(theta2) is proportional to sin(theta1). We can use this fact to solve for sin(theta2) when theta1 = 58.0 degrees:

sin(theta2)/sin(theta1) = sin(theta2)/sin(58.0 degrees) = constant

So, when theta1 = 32.0 degrees:

sin(theta2)/sin(32.0 degrees) = sin(theta2)/sin(58.0 degrees)

sin(theta2) = (sin(32.0 degrees)/sin(58.0 degrees))*sin(theta1)

sin(theta2) = (0.5299)*sin(32.0 degrees)

theta2 = sin^-1[(0.5299)*sin(32.0 degrees)]
       = 19.3 degrees

Therefore, the angle of refraction when the incident angle is 32.0 degrees is 19.3 degrees.

If Light Reflected from a Transparent Substance at an Angle