Question

To understand polarization of light and how to use Malus's law to calculate the intensity of a beam of light after passing through one or more polarizing filters.

The two transverse waves shown in the figure(Figure 1) both travel in the +z direction. The waves differ in that the top wave oscillates horizontally and the bottom wave oscillates vertically. The direction of oscillation of a wave is called the polarization of the wave. The upper wave is described as polarized in the +x direction whereas the lower wave is polarized in the +y direction. In general, waves can be polarized along any direction.

Recall that electromagnetic waves, such as visible light, microwaves, and X rays, consist of oscillating electric and magnetic fields. The polarization of an electromagnetic wave refers to the oscillation direction of the electric field, not the magnetic field. In this problem all figures depicting light waves illustrate only the electric field.

A linear polarizing filter, often just called a polarizer, is a device that only transmits light polarized along a specific transmission axis direction. The amount of light that passes through a filter is quantified in terms of its intensity. If the polarization angle of the incident light matches the transmission axis of the polarizer, 100% of the light will pass through, so the transmitted intensity will equal the incident intensity. More generally, the intensity of light emerging from a polarizer is described by Malus's law:

I=I0cos2θ,

where I0 is the intensity of the polarized light beam just before entering the polarizer, I is the intensity of the transmitted light beam immediately after passing through the polarizer, and θ is the angular difference between the polarization angle of the incident beam and the transmission axis of the polarizer. After passing through the polarizer, the transmitted light is polarized in the direction of the transmission axis of the polarizing filter.

PART E

A beam of unpolarized light with intensity I0 falls first upon a polarizer with transmission axis θTA,1 then upon a second polarizer with transmission axis θTA,2, where θTA,2−θTA,1=90degrees (in other words the two axes are perpendicular to one another). What is the intensity I2 of the light beam emerging from the second polarizer? (Figure 4)

Express your answer as a decimal number times the symbol I0. For example, if I2=(1/4)I0, enter 0.25 * I_0.

Answer 1

The system of polarized light is given as initial intensity of light is I_0 angle b/w analyzer and polarizer is 90 degree i.e. theta = 90 degree S0, Intensity of light observed by malus law is I_2 = I_0 cos^2 theta or I_2 = I_0 cos^2 90 degree or I_2 = 0