Physics · Ch 6 — Optics
Brewster's Law
Brewster's Law
In 1808, Malus discovered that ordinary light reflected off a transparent surface is partially plane polarised, with the extent of polarisation depending on the angle of incidence; at one particular angle, the reflected light is found to be completely plane polarised, called the polarising angle or Brewster's angle . Sir David Brewster, a British physicist, further found that at this particular angle of incidence, the reflected ray and the refracted (transmitted) ray are exactly perpendicular to each other: , so . Substituting into Snell's law, , gives Brewster's law: -- the tangent of the polarising angle for a transparent medium equals its refractive index. For glass (), ; for water (), …
Worked out. Applying Brewster's law tan(ip) = n directly: for glass, n = 1.5, giving ip = tan inverse(1.5) = 56.3 degrees; for water, n = 1.33, giving ip = tan inverse(1.33) = 53.1 degrees. Both results confirm the general trend that a higher refractive index gives a larger polarising angle, and both angles fall well within the practically achievable range for a tabletop reflection-polar …
Worked out. For unpolarised light travelling horizontally to be reflected as plane polarised light off a glass plate of refractive index 1.65, the plate must be positioned so the light strikes it at exactly the polarising angle. Using Brewster's law, ip = tan inverse(1.65) = 58.8 degrees is the required angle of incidence, measured from the normal. Since the incident light is horizontal, the plate's own surface -- and hence its normal -- must be tilted so that this normal makes exactly 58.8 degrees with the horizontal beam; equivalently, the plate's surface itself must be inclined at (90 - 58.8) = …