OpenWorldLab

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Polarisation

Brewster’s angle

Glass reflects a few per cent of the light that hits it, but at one angle it reflects none of the light polarised in the plane of incidence. That angle is Brewster’s angle, and lasers use it to choose their polarisation.

What you are looking at

The laser is horizontally polarised: in the table’s plane, which is the plane of incidence. The glass block sits at 56.6°, Brewster’s angle for BK7 at 632.8 nm, and the power meter where the reflection would go reads nothing.

How the bench is set up

Laser polarised horizontally (p), a 10 mm BK7 block at 56.6°, a power meter in the reflected direction and a beam dump for the transmitted beam.

The theory

Fresnel’s equations give the p-reflectance

Rp=∣ncos⁡θi−cos⁡θtncos⁡θi+cos⁡θt∣2,R_p = \left|\frac{n\cos\theta_i - \cos\theta_t}{n\cos\theta_i + \cos\theta_t}\right|^2,

which vanishes when the reflected and refracted rays are at right angles, at

tan⁡θB=n.\tan\theta_B = n.

What to measure

p-reflectance vanishes at tan θ_B = n

  1. Note the meter reading: zero at Brewster’s angle.
  2. Switch the laser to vertical (s) polarisation. The front face reflects about 15%, and the back face sends most of that again out alongside it, so the meter reads about a quarter of the beam.
  3. Turn the glass by a degree or two each way and see p-reflection rise from zero.

What the model leaves out

  • The glass surface is perfectly clean and flat.

Things to try

  • Change the glass to N-SF11 (n ≈ 1.78): the angle moves to about 60.7°.

References

  • E. Hecht (2017), Optics, 5th edition, Pearson.
  • D. Brewster (1815), On the laws which regulate the polarisation of light by reflexion from transparent bodies, Philosophical Transactions 105, 125.

More experiments, and how the lab works, are in the laser lab’s overview.