Malus's Law

Malus's Law allows us to calculate the intensity of polarized light that passes through a polarizing filter oriented at some angle to the plane of polarization of the light. This is illustrated below. Unpolarized light passes through a polarizing filterHaving passed through the filter as shown, the light is vertically polarized – in fact though electromagnetic maves have both electric and magnetic components oscillating at right angles, it is the electric component that is polarized in the polarizing plane, with the magnetic field oscillating at right angles still.

If the polarized light has intensityafter passing throughis made to pass through a second filterthen the intensity of the light after passing throughis given bywhere is the angle between the planes of the polarizing filters.

Notice that the intensity of light is at all times proportional to the square of the amplitude, so that if, after passing through the polarizing filterthe light has amplitudeand after passing through polarizing filterthe light has amplitudethenand squaring both sides of this equation gives (1), withand