Q.Explain what is Brewster's law.

When unpolarised light hits a transparent surface — say, a glass window or a still water surface — the reflected light is usually a messy mixture of vibrations. But at one very particular angle of incidence, something clean happens: the reflected light becomes perfectly polarised, with its electric field vibrating in only one direction. That angle is Brewster's angle.

The intuition: why does this happen?

Think of light as a transverse wave — its electric field oscillates perpendicular to the direction it travels. When light strikes a surface, the electrons in the material are forced to oscillate by the incoming wave. These oscillating electrons then re-radiate light, which is what we see as the reflected and transmitted (refracted) beams.

Now, an oscillating electron cannot radiate energy along the direction of its own oscillation. If the electron is jiggling up and down, it sends no light straight along the up-down axis. This is the key.

At a certain angle, the reflected ray and the refracted ray become perpendicular. At that exact geometry, the direction of the reflected ray coincides with the direction in which the electrons in the material would be oscillating (for one particular polarisation). Those electrons therefore cannot radiate in that direction — so that polarisation component is completely absent from the reflected beam. The reflected light then contains only the other polarisation component, making it perfectly plane-polarised.

The precise statement

Brewster's angle $\theta_B$ is the angle of incidence at which light reflected from a transparent medium is completely plane-polarised. It satisfies

where $n$ is the refractive index of the medium (relative to the incident medium, usually air with $n \approx 1$).

At this angle, two conditions hold simultaneously:

1. The reflected light is completely plane-polarised with its electric field perpendicular to the plane of incidence (i.e., parallel to the surface).
2. The reflected ray and the refracted ray are perpendicular to each other.

Why the perpendicular condition is not a separate fact

The two results — polarisation and perpendicular rays — are actually the same physics. When the reflected and refracted rays are perpendicular, the reflected ray points exactly along the direction of the dipole oscillation that would be caused by the refracted ray's electric field. That oscillation cannot radiate along its own axis, so that polarisation is missing from the reflection. The perpendicular condition is the geometric expression of the polarisation condition.

A concrete example

For glass with $n = 1.5$, Brewster's angle is …