Polarisation, Malus's Law and Brewster's Law

First identify whether the incident light is unpolarised or already plane-polarised. For unpolarised light, use I0/2 after the first polariser because only one vibration plane is selected. For plane-polarised light through an analyser, resolve the field component along the analyser axis and use I = I₀ cos^2 theta. For Brewster-angle questions, use tan theta_B = n and state the final geometry cue: reflected and refracted rays are at 90 degree to each other.

A diagram is useful when showing polariser and analyser axes, unpolarised light becoming plane-polarised light, and Brewster-angle reflection. Labels should include transmission axis, analyser angle theta, reflected ray, refracted ray and 90 degree angle between reflected and refracted rays at Brewster's angle.

A common wrong answer uses sin^2 theta in Malus's law. The transmitted component is along the analyser axis, so the intensity varies as cos^2 theta.

Polarisation is the restriction of light vibrations to one plane perpendicular to the direction of propagation. It proves that light waves are transverse.

Polarisation is the restriction of light vibrations to one plane perpendicular to the direction of propagation. It proves that light waves are transverse. Malus's law assumptions: the incident light on the analyser is plane-polarised and the analyser is ideal. Key step: resolve the electric-field amplitude along the analyser axis, E = E0 cos theta; since intensity is proportional to E^2, the final result is I = I₀ cos^2 theta. Brewster's law result: tan theta_B = n for incidence from air, with reflected and refracted rays perpendicular at theta_B. Intensities are in W m^-2 and refractive index has no SI unit. Polaroid sunglasses reduce glare from horizontal surfaces because reflected glare is strongly polarised and the lenses block much of that vibration direction.

Ordinary light has electric-field vibrations in many planes perpendicular to the direction of travel. A polariser transmits vibrations along its transmission axis and blocks the perpendicular component. When polarised light passes through an analyser, the transmitted intensity depends on the angle between their transmission axes. Reflection can also produce plane-polarised light at Brewster's angle. Malus's law assumptions: the incident light on the analyser is plane-polarised and the analyser is ideal. Key step: resolve the electric-field amplitude along the analyser axis, E = E0 cos theta; since intensity is proportional to E^2, the final result is I = I₀ cos^2 theta. Brewster's law result: tan theta_B = n for incidence from air, with reflected and refracted rays perpendicular at theta_B. Intensities are in W m^-2 and refractive index has no SI unit. Plane-polarised light of intensity 80 W m^-2 enters an analyser with its axis at 30 degree to the vibration direction. I = I₀ cos^2 theta = 80 x cos^2 30 degree = 80 x 3/4 = 60 W m^-2. The analyser transmits 60 W m^-2. It is asked as proof of transverse nature, Malus's-law numerical, Brewster-angle calculation, or conceptual questions on glare reduction and crossed polaroids. A common wrong answer uses sin^2 theta in Malus's law. The transmitted component is along the analyser axis, so the intensity varies as cos^2 theta.