Polarisation
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Direct answer
Glare from a sunlit lake can be wiped out by polaroid sunglasses while the rest of the scene survives — proof that light's oscillations are confined to selected planes. Ordinary light is unpolarised, its electric field vibrating in every direction perpendicular to propagation; a polariser passes only one plane, halving the intensity. A second polariser (analyser) then transmits I = I0 cos^2 θ by Malus's law, so crossed polarisers at 90 degrees pass nothing. At Brewster's angle, tan ip = n, reflected light becomes completely polarised with ip + r = 90 degrees — about 56.3 degrees for glass of n = 1.5. Sound, being longitudinal, cannot be polarised — the very fact that certifies light transverse.
What you must remember
- The transverse certificate: only transverse waves can be polarised; the polarisation of light is the experimental proof that light is transverse, while audible sound shows no polarisation.
- Polariser action: unpolarised light through a polariser emerges plane-polarised with intensity exactly I0/2 — no dependence on the polariser's orientation.
- Malus's law: I = I0 cos^2 θ between two polarisers; θ = 0 passes all, θ = 90 degrees (crossed) passes none.
- Brewster's law: n = tan ip; at this angle the reflected ray is completely polarised (perpendicular to the plane of incidence) and the reflected and refracted rays are perpendicular, ip + r = 90 degrees.
- Numerical anchor: glass with n = 1.5 gives ip ≈ 56.3 degrees; water with n = 1.33 gives about 53 degrees.
- Scattering polarisation: sunlight scattered by the atmosphere at 90 degrees to the sun's direction is partially polarised — why the sky photographed through a rotated polaroid brightens and dims, and why bees navigate by it.
- Applications: polaroid sunglasses block horizontally polarised glare from water and roads; LCD screens switch pixels by rotating polarisation; photoelasticity maps stress in transparent models through polarisation fringes.
- Distinguishing pair: intensity after one polariser is I0/2 (unpolarised input); after two, I0/2 cos^2 θ — questions live on this difference.
Two polarisers, one calculation, both regimes
Unpolarised light of intensity I0 meets a polariser; whatever the polariser's orientation, the transmitted beam carries I0/2 plane-polarised. An analyser follows at θ = 60 degrees: Malus gives I = (I0/2) cos^2 60 degrees = (I0/2)(1/4) = I0/8. Rotate the analyser to 90 degrees and the chain goes dark — crossed polarisers, the state every LCD exploits by rotating the plane instead. Now set the first polariser's plane vertically and pass the beam through a glass plate at Brewster incidence instead: the reflected component is already completely polarised perpendicular to the incidence plane, so a polaroid held to accept it passes the full glare, and one held at 90 degrees to it kills the reflection entirely — the working principle of camera polarising filters.
Where the exam polarises its candidates
The first separator is the halving rule: a question asking for transmitted intensity after one polariser tempts candidates to apply cos^2 θ — but θ is undefined for unpolarised light, and the answer is always I0/2 regardless of rotation. The second is Brewster's geometry: at ip the reflected ray is completely polarised and the refracted ray only partially so, and the two rays are exactly perpendicular — a question showing "reflected ray polarised in the plane of incidence" is false by definition, since the polarisation is perpendicular to that plane. Third, the two-frame trap: rotating a single polariser in unpolarised light changes nothing in intensity, while rotating it in polarised light produces two maxima and two extinctions per revolution — the standard laboratory test to tell whether incident light is already polarised. Finally, sound questions close the loop: longitudinal waves have no transverse vibration to select, so no polariser exists for audio — the assertion-reason pairing that seals the transverse-nature argument for light.
Frequently asked questions
What proves that light is a transverse wave?
Light can be polarised — its vibrations can be confined to one plane — and only transverse waves admit this; longitudinal waves such as sound cannot be polarised.
What fraction of unpolarised light passes through a single polariser?
Exactly half, I0/2, independent of the polariser's orientation, because averaging cos^2 over all planes gives one-half.
What does Malus's law state?
The intensity transmitted by an analyser from plane-polarised light is I = I0 cos^2 θ, where θ is the angle between the light's polarisation plane and the analyser's pass axis.
What is special about Brewster's angle?
At incidence tan ip = n, the reflected light becomes completely polarised perpendicular to the plane of incidence, and the reflected and refracted rays are at 90 degrees to each other.
Why do polaroid sunglasses reduce glare from roads and water?
Sunlight reflecting off horizontal surfaces becomes partially horizontally polarised, and the sunglasses' vertically oriented polarising axis blocks that component while passing the rest of the scene.