Unpolarized light has electric-field vibrations in many directions perpendicular to propagation, while polarized light has the electric field limited to one direction in that plane.

• The plane of oscillation contains the electric-field vibration, while the plane of polarization is perpendicular to it.
• Only transverse waves can be polarized, which is why polarization proves the transverse nature of light.
• Trap: confusing the plane of oscillation with the plane of polarization because their names sound similar.

Malus law gives I = I0 cos^2 theta and A = A0 cos theta for polarized light passing through an analyzer at angle theta to the transmission axis.

• If theta = 0 degree, the analyzer passes the entire polarized beam; if theta = 90 degrees, the transmitted intensity is zero.
• For unpolarized light passing through the first polarizer, the intensity becomes Ii/2 before Malus law is applied at the analyzer.
• Trap: using I = I0 cos theta instead of cos^2 theta for intensity.

Plane polarized light can be produced by reflection at Brewster's angle, by dichroism, by double refraction, by Nicol prism, and by scattering in the right direction.

• Brewster's law gives mu = tan theta_p and at that angle the reflected and refracted rays are perpendicular.
• In double refraction, the O-ray obeys Snell's law while the E-ray does not, and the two rays have perpendicular polarizations.
• Trap: treating every polarizer as if it works only by Malus law rather than by a distinct physical production mechanism.

Optical activity rotates the plane of polarization, and the specific rotation is [alpha]^lambda_T = theta/(L x C) for a given wavelength and temperature.

• Dextro-rotatory substances rotate clockwise when viewed against the direction of propagation, while laevo-rotatory substances rotate anticlockwise.
• Optical activity is linked to molecular or crystal asymmetry, not to simple absorption of light.
• Trap: confusing optical activity with dichroism, which selects one vibration direction rather than rotating it.

Polarization is used in glare reduction, LCD displays, photoelasticity, 3D imaging, solar-compass navigation, and optical-activity studies of molecules and crystals.

• A polarimeter measures optical rotation and helps identify specific rotation in active substances.
• Glare reduction works because reflected light is often preferentially polarized and can therefore be filtered.
• Trap: memorizing only sunglasses and missing the science applications such as stress analysis or molecular asymmetry studies.