How to Calculate Brewster's Angle

By Carlos Mano
Calculating Brewster's angle

When light strikes a surface, part of the light is reflected and part of the light penetrates (refracts). The relative amounts of this reflection and refraction depend on the substances the light is passing through and also on the angle that the light strikes the surface. There is an optimum angle--depending on the substances--that will allow the maximum refraction (penetration). This optimum angle is known as Brewster's angle after the Scottish physicist David Brewster.



Calculate Brewster's angle for ordinary polarized white light using the formula: theta = arctan (n1/n2) where theta is Brewster's angle and n1 and n2 are the refraction indexes of the two media.

Calculate the best angle for light to strike glass for maximum penetration. From a table of refraction indexes find that the refraction index for air is 1.00 and the refraction index for glass is 1.50. Brewster's angle will be arctan (1.50/1.00) = arctan (1.50) = 56 degrees (approximately).

Calculate the best angle for light to strike water for maximum penetration. From a table of refraction indexes find that the refraction index for air is 1.00 and the refraction index for water is 1.33. Brewster's angle will be arctan (1.33/1.00) = arctan (1.33) = 53 degrees (approximately).

Tip

Air is the standard for refraction indexes, so the refraction index for air is 1.0. In most cases we are interested in light that is traveling through air to strike a surface. In these cases we can use the slightly simpler equation theta = arctan (r) where theta is Brewster's angle and r is the refraction index of the impacted surface.

Warning

Brewster's angle shifts slightly if the light is colored or polarized.