Polarisation by Reflection – From Intuition to the Law
Imagine sunlight hitting the surface of a still lake. You see a glare — that harsh, bright reflection that makes it hard to see the fish below. Now put on polarised sunglasses and tilt your head. The glare vanishes. What just happened? The sunglasses blocked something that the reflection had done to the light.
That something is polarisation.
What does "polarisation" even mean?
Light is a transverse wave — the electric field oscillates perpendicular to the direction the light travels. In ordinary (unpolarised) light, the electric field vibrates in every possible direction perpendicular to the ray, all at once. Think of it like a skipping rope being shaken randomly in all sideways directions.
When light reflects off a surface, something interesting happens: the surface "filters" these vibrations. Certain directions of vibration get reflected more strongly than others. The reflected light is no longer vibrating in all directions — it is now partially polarised, and at one special angle, completely polarised.
The key intuition: the surface is picky
When light hits a boundary between two media (say, air and glass), the electrons in the glass are set into oscillation by the incoming electric field. These oscillating electrons then re-radiate light — that re-radiated light is the reflected beam.
But here is the crucial point: an oscillating electron cannot radiate along its own direction of oscillation. If the electron is vibrating up-and-down, it sends no energy straight along that up-down line.
Now, at a particular angle of incidence, the reflected ray and the refracted ray are perpendicular to each other. At that exact geometry, the direction of vibration that is parallel to the plane of incidence (call it the "p-polarisation") would require the electrons to radiate along their own oscillation direction — which they cannot do. So that component is completely suppressed. Only the vibration perpendicular to the plane of incidence (the "s-polarisation") survives.
The result: the reflected light is 100% plane-polarised, with its electric field vibrating perpendicular to the plane of incidence.
The precise statement
When unpolarised light is reflected from a transparent surface (like glass or water), the reflected light is completely plane-polarised if the angle of incidence θi satisfies
tanθB=n1n2
where n1 is the refractive index of the incident medium and n2 that of the transmitting medium. This angle θB is called Brewster's angle.
At Brewster's angle, the reflected and refracted rays are exactly 90∘ apart. The reflected beam contains only the component of light whose electric field is perpendicular to the plane of incidence.
What about other angles? …