Electromagnetic radiation from an incandescent source, such as a light bulb, is unpolarized, which means that the electric field of the wave points in random directions perpendicular to wave travel. One way to produce polarized radiation involves applying an alternating voltage to a straight piece of wire to form an antenna (See figure below). Radiation is emitted from the antenna perpendicular to the wire with a polarization which is parallel to the wire.
In this diagram the small arrows show the direction of the electric field, and the large arrows show the direction of the wave.
Another way to obtain polarized radiation involves allowing unpolarized radiation to be incident on a film or material which transmits radiation of one polarization but absorbs radiation of the perpendicular polarization. Such a film is called a polarizer. If unpolarized light of intensity I0 is incident on a vertical polarizer, the radiation that passes through is vertically polarized with intensity 1/2 I0. The figure below shows this schematically.
If polarized radiation is incident on a polarizer, the amount of energy that is transmitted depends on the relative angle of the radiation polarization and the polarizer axis. If they are aligned, then all the radiation is transmitted. If the angles differ by θ, then the intensity of the transmitted radiation is cos2θof the original intensity.
All of the foregoing refers to ideal polarizers. All manufactured polarizers have less than ideal efficiency which comes from reflection off the two surfaces and absorption of the parallel component.
In questions 1–4, an unpolarized radiation source is incident on a series of polarizers. Without the polarizers the intensity of the source is I0. Assume the polarizers are ideal.
An optically active substance is a substance which rotates the plane of polarization of a beam. The figure shows a modification of the figure in Problem 2, with an optically active substance between the polarizers. What is the intensity of the resultant beam?