Polarization

Light is a transverse electromagnetic wave and can be polarized — meaning its electric field oscillates in a definite direction. Polarizers, Brewster angles, and birefringent materials allow precise control of polarization state.

Key Concepts

Malus's law: I = I₀cos²θ
Brewster's angle: tanθ_B = n₂/n₁
Birefringent materials have two refractive indices (ordinary and extraordinary)
Quarter-wave plates convert linear to circular polarization
Unpolarized light through one polarizer: I = I₀/2

Key Equations

Malus's law

I = I_0\cos^2\theta

Brewster's angle

\tan\theta_B = \frac{n_2}{n_1}

Phase retardation

\delta = \frac{2\pi}{\lambda}(n_e - n_o)d

Quarter-wave plate

\delta = \frac{\pi}{2} \Rightarrow d = \frac{\lambda}{4(n_e - n_o)}

Worked Example

Example Problem

Problem

Find Brewster's angle for light going from air (n=1) into glass (n=1.5).

Solution

tanθ_B = n₂/n₁ = 1.5/1 → θ_B = arctan(1.5) = 56.3°.

Practice

Exercises

7 problems

1 of 7

Unpolarized light (I₀=100 W/m²) passes through a polarizer. Find the transmitted intensity in W/m².

Your answer

W/m²

2 of 7

Linearly polarized light (100 W/m²) passes through a polarizer at 45°. Find the transmitted intensity using Malus's law.

Your answer

W/m²

3 of 7

Find Brewster's angle (degrees) for light going from water (n=1.33) into glass (n=1.5).

Unlock Exercise 3