Question

Light of original intensity I0 passes through two ideal polarizing filters having their polarizing axes oriented as shown in the figure (Figure 1). You want to adjust the angle ϕ so that the intensity at point P is equal to I0/8.00.

A.)If the original light is unpolarized, what should ϕbe?

B.)If the original light is linearly polarized in the same direction as the polarizing axis of the first polarizer the light reaches, what should ϕ be?

Answer 1

General formula: When light of intensity having electric field vector oriented at angle to the polarization axis of a polarizer pases through the polarizer the intensity of the emergent light is given by , the electric field vector being oriented in the direction same as the polarizing axis.

A) For an unpolarized light the electric field vectors are oriented in all directions from to . When such unpolarized light of intensity passes through a polarizer the intensity of the polarized light is given by the average of over to .

Thus the light intensity after passing the first polarizer is . After passing the second polarizer the intensity becomes .

When the intensity at P is , the is given by

B) If the original light of intensity is linearly polarized in the same direction as the polarizing axis of the first polarizer then the intensity of light after passing the first polarizer is still .

After passing the second polarizer the intensity is

The intensity after passing the second polarizer is