Polarisation

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Concept 1

Polarisers and analysers

Learn this word for word

Plane-polarised light: "The electric vector of light oscillates in a single plane."

Watch out: marking instructions do NOT accept "travels in a single plane/direction" or "oscillates in one direction" — it must be the electric vector, and it must be a plane.

Unpolarised light vibrates in every plane. A polariser only lets through the component vibrating in one plane, so its output is plane-polarised. A second polarising filter used to test the light is called an analyser.

  • Plane-polarised light through a rotating analyser: brightness starts at a maximum, falls to a minimum at 90°, rises back to a maximum at 180°.
  • Unpolarised light through a rotating analyser alone: brightness stays constant.
Concept 2

Brewster's angle

Unpolarised light hitting an insulator's surface at one particular angle of incidence — Brewster's angle, ip — reflects as fully plane-polarised light. At that angle, the reflected and refracted rays are at 90° to each other.

Brewster's law
n = tan ip
refractive index from the polarising angle
The derivation
i_p + r = 90° (reflected and refracted rays are at 90°; angle of reflection = i_p) r = 90° − i_p (rearranging) sin i_p = n sin r (Snell's law, air into the insulator) sin i_p = n sin(90° − i_p) (substituting r) sin i_p = n cos i_p (sin(90° − x) = cos x) n = tan i_p
Substitute & solve
Calculate the Brewster angle for light reflected from water (n = 1.33). 3 marks
n=tan ip
tan ip=1.33
ip=53.1°
Substitute & solve
A teacher determines Brewster's angle for Perspex (n = 1.49). Calculate it. 3 marks
n=tan ip
tan ip=1.49
ip=56.1°
Practice 1

Glass has a refractive index of 1.52. Calculate Brewster's angle for glass. 3 marks

Answer
n = tan i_p tan i_p = 1.52 i_p = 56.7°

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Sources & credits: notes written by Mr Stewart. Past-paper questions and marking instructions reproduced for educational use, © Qualifications Scotland (SQA).