If a linearly polarized light is incident on a Polaroid with the E-vector (electric field vector) parallel to the transmission axis, the light is completely transmitted by the Polaroid. If the E-vector (electric field vector) perpendicular to the transmission axis, the light is completely stopped by the Polaroid. If the E-vector (electric field vector) is at an angle θ to the transmission axis, the light is partially transmitted. The intensity of partially transmitted light (by the Polaroid) is
I = I0cos²θ
I0 is the intensity when the incident E-vector is parallel to the transmission axis.
(Polaroids have long chains of hydrocarbons which become conducting at optical frequencies. When light falls perpendicularly on the sheet, the electric field parallel to the chains is absorbed but the field perpendicular to the chains gets transmitted. The direction perpendicular to the chains is called the transmissiona axis of the Polaroid.
(Chapter Light waves)