Intensity of unpolarized light (Malus' law)


Light as one type of electromagnetic (EM) wave, is a transverse wave, consisting of varying electric and magnetic fields that oscillate perpendicular to the direction of propagation.
Polarization is the attribute that a wave’s oscillations have a definite direction relative to the direction of propagation of the wave. Waves having such a direction are said to be polarized. For an EM wave, we define the direction of polarization to be the direction parallel to the electric field.
The axis of a polarizing filter is the direction along which the filter passes the electric field of an EM wave. Only the component of the EM wave parallel to the axis of a filter is passed.
If the angle between the direction of polarization and the axis of a filter is “theta”, the intensity of the transmitted part of the wave is proportional to the intensity of the the polarized wave before passing through the filter.
A beam of unpolarised light can be thought of as containing a uniform mixture of linear polarizations at all possible angles. (cos(θi)= 1/2)

Related formulas


IIntensity of the transmitted wave (W/m2)
I0Intensity of the polarized wave before passing through the filter (W/m2)