Question

Polarized light is to have its polarization plane rotated by 90 degrees. In which of the following cases does the final beam have the greatest intensity?

Select one:

a. 1 polarizing filter, rotating the beam by 90 degrees

b. 3 polarizing filters, both rotate the beam by 30 degrees

c. 6 polarizing filters, each rotating the beam by 15 degrees

d. None of the above, polarized light can't be rotated

please explain the answer think it is C.

Answer 1

According to Malus law, the intensity of a polarized light when passed through a polarizer whose transmission axis makes angle θ with the polarization of incident light is given by

​​​​​(a) The transmission axis of the polarizer makes angle 90° with the polarization of the incident light. The intensity of the transmitted light is

(b) There are three polarizers. The first polarizer makes angle 30° with the polarization of the incident light. The intensity of the light passing through the first polarizer is

The second polarizer makes angle 30° with the first polarizer. The output light from the first polarizer is incident on the second polarizer. The intensity of the output light from the second polarizer is

Using the above equation for I_{​​​​​​1} we have

Similarly, the light output of the third polarizer is

Using above equation for I_{​​​​​​2} we have

(c)

The transmission axis of each polarizer makes angle 15° with the previous polarizer. Following the same procedure as in part (b), the intensity of output light is

Therefore the intensity of the output is the greatest in part (c).