Polarization and the Reflection and Refraction of Light?

Question

Light is reflected from a glass coffee table. When the angle of incidence is 58.0°, the reflected light is completely polarized parallel to the surface of the glass. What is the index of refraction of the glass?

Answer 1

You are describing Brewster's angle for the glass-to-air interface. This is where the reflected ray is perpendicular to the refracted ray. A simple refraction diagram will show that this means:

theta_refracted = 90 - theta incident

Refraction follows the relationship:

n * sin(theta_refracted) = sin(theta_incident)

Combining these shows that:

n = sin(theta_incident) / sin(theta_refracted)
n = sin(theta_incident) / sin(90-theta_incident)
n = sin(theta_incident) / cos(theta_incident)
n = tan(theta_incident)
n = tan(58 degrees)
n = 1.6003

(Note: n=1.18 is not correct, since this is not a "critical angle" problem)

Answer 2

At this critical angle x2=90, x1=the Brewster angle

n1*sin(x1)=n2*sin(x2)
n1=1
so1*sin(90)=n2*sin(58) ==>n2=1/sin(58)=1.18