   Chapter 27, Problem 97PE

Chapter
Section
Textbook Problem

If θ b 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, prove that θ b + θ ' b = 90.0 ° .

To determine

Prove that θb+θb'=90°

Explanation

Given info:

Refractive index of air, n1=1

Brewster angle, θb=55.6

Formula used:

The refractive light will be completely polarized at angle θ is given by

tanθ=n2n1

Here,

n2 is the refractive index of media

n2 is the refractive index of media in which incident and reflected light travel

Calculation:

Let the refractive index of two substance are n1 and n2 respectively.

When the light is reflected from the top surface than the Brewster angle is calculated as

tanθb=n2n1θb=tan1 n 2 n 1...... (1)

When the light is reflected from the bottom surface than the Brewster angle is calculated as

tanθb'=n1n2θb'=tan1 n 1 n 2...... (2)

Adding equation (1) and 2)

θb+θb'=tan1 n 2 n 1+tan1 n 1 n 2θb+θb'=tan

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