Question

If θb is Brewster’s angle for light reflected from the top of an interface between two substances, and θ′b is Brewster’s angle for light reflected from below, what relationship holds true between these angles?

a) θb + θ′b = 90.0°
b) θb - θ′b = 90.0°
c) θb × θ′b = 90.0°
d) θb / θ′b = 90.0°

Answer 1

The relationship between Brewster's angle from the top of an interface (θb) and from the below (θ'b) is that their sum equals 90 degrees, as reflected and transmitted rays are perpendicular at Brewster's angle.

Step-by-step explanation:

When talking about Brewster's angle, it refers to the incident angle at which light with a particular polarization is perfectly transmitted through a transparent boundary between two substances, with no reflection. Brewster's law states that the reflection will be 100% polarized in a direction parallel to the surface. The law can be mathematically expressed using the refractive indices of the two media (n1 for the incident medium and n2 for the other) involved as θb = arctan(n2/n1).

Considering light reflecting off the interface from the top and from below, Brewster's angle θb for the top interface and θ'b for the bottom interface will adhere to the relationship θb + θ'b = 90.0°. This is true because when light reflects at Brewster's angle, the transmitted and reflected rays are perpendicular to each other. Thus, if we consider the angles of incidence and transmission from both sides of the interface, they add up to 90 degrees.