Polarization

Polarization

1. What Polarization Is

Polarization = orientation of electric field vector $E$ oscillations perpendicular to propagation. Light is transverse EM wave; $E$ can oscillate in one plane (polarized) or randomly (unpolarized natural light).

• Unpolarized: $E$ rotates randomly in plane ⊥ $k$ (superposition of two orthogonal incoherent components).
• Linearly polarized: $E$ oscillates in one fixed plane (e.g., vertical).
• Circular/elliptical: $E$ tip traces circle/ellipse as wave propagates (phase difference ±90° between components + equal/unequal amplitudes).

2. How to Produce Polarization

• Selective absorption: Polaroid sheet (dichroism).
• Reflection: Brewster's angle $tanθ_B = μ$ gives reflected ray fully polarized ⊥ plane of incidence.
• Refraction / double-refraction: Nicol prism / calcite separates $o$ and $e$ rays (next topics).
• Scattering: sky light polarized.

3. Malus's Law

Polarizer at angle $θ$ to incident linearly polarized beam $E_0$:

For unpolarized $I_0$ incident, first polarizer gives $I =I_0/2$ (average $cos²=1/2$), second polarizer then obeys Malus with $θ$ between them.

4. Worked Examples

(a) Unpolarized I0 through polarizer → I1=I0/2 ; through second polarizer at 60° ⇒ I2=I1 cos²60= I0/8 ✓

(b) Brewster angle for glass μ=1.5: θ_B= arctan1.5≈56.3°; reflected at that angle is polarized.

(c) Need to distinguish polarized vs unpolarized? Rotate Polaroid: polarized shows variation I0 cos²θ → zero at 90°, unpolarized remains I0/2 constant.

5. Uses

3D glasses (orthogonal polarizations), LCD (polarizers + liquid crystal rotation), glare reduction, stress analysis (photoelasticity).

6. Exam Points

• Define polarization, show $E$ ⊥ $k$ — 3 marks, very frequent.
• Types: unpolarized, linear, circular, elliptical with diagram — 5 marks, very frequent.
• Malus's law $I=I_0 cos²θ$ and $I=I_0/2$ for unpolarized — 5 marks, very frequent.
• Brewster's law $tanθ_B=μ$ — 3-5 marks, frequent.