Unpolarized Light (UPL): Vibrations occur in all directions perpendicular to propagation.
Linearly/Plane Polarized Light (PPL): Vibrations confined to a single plane.
Circularly Polarized Light (CPL): Two PPLs of equal amplitude and $\lambda/4$ phase difference, electric vector rotates in a circle.
Elliptically Polarized Light (EPL): Two PPLs of unequal amplitude and $\lambda/4$ phase difference, electric vector traces an ellipse.
Partially Polarized Light (PRPL): Neither fully polarized nor fully unpolarized.

If unpolarized light passes through a polarizer and then an analyzer, the intensity of the transmitted light ($I_\theta$) varies with the angle ($\theta$) between their optic axes.
$I_\theta = I_0 \cos^2\theta$
- $I_0$: maximum intensity (when axes are parallel, $\theta=0^\circ$).
- Maximum intensity at $0^\circ, 180^\circ, 360^\circ$.
- Minimum intensity (zero) at $90^\circ, 270^\circ$.

By Reflection (Brewster's Law):
- When unpolarized light is incident at Brewster's angle ($i_p$), the reflected light is completely plane-polarized.
- The reflected and refracted rays are perpendicular ($i_p + r_p = 90^\circ$).
- Brewster's Angle: $\mu = \tan i_p$
By Pile of Plates: Multiple reflections from a stack of glass plates at Brewster's angle.
By Double Refraction: Splitting of unpolarized light into two linearly polarized beams (O-ray and E-ray) whose vibrations are mutually perpendicular.

Occurs in anisotropic crystals (e.g., Calcite, Quartz).
Ordinary Ray (O-ray): Obeys Snell's law, constant velocity, spherical wavefront, vibrations perpendicular to optic axis.
Extraordinary Ray (E-ray): Does not obey Snell's law, velocity varies with direction, ellipsoidal wavefront, vibrations parallel to optic axis.
Uniaxial Crystals: Have one optic axis (e.g., Calcite, Quartz).
- Negative Crystals (e.g., Calcite): $\mu_O > \mu_E$ (O-ray is slower), $\Delta\mu = \mu_E - \mu_O < 0$.
- Positive Crystals (e.g., Quartz): $\mu_E > \mu_O$ (E-ray is slower), $\Delta\mu = \mu_E - \mu_O > 0$.
Biaxial Crystals: Have two optic axes (e.g., Mica, Borax).

Polarizer: An optical device that produces polarized light from unpolarized light.
- Nicol Prism: Eliminates O-ray via Total Internal Reflection, transmits PPL (E-ray).
- Polaroids: Eliminate O-ray via selective absorption (dichroism).
- Tourmaline Crystal: Exhibits dichroism, used as a polarizer.
Analyzer: A polarizer used to detect or analyze polarized light.

Each point on the refracting surface acts as a source of two secondary wavefronts (O-wavefront and E-wavefront).
O-wavefront is spherical, E-wavefront is ellipsoidal.
Velocities of O-ray and E-ray are equal along the optic axis.

Doubly refracting uniaxial crystal plates that introduce a phase difference ($\Phi$) between O-ray and E-ray.
$\Phi = (\mu_O - \mu_E)t$ (path difference).
Quarter Wave Plate (QWP): Introduces a phase difference of $\pi/2$ (path