Question

7. A single photon, from an unpolarized source, traveling in the z direction is directed through a series of three polarizers: first a polarizer with its axis in the x direction, then a polarizer at 25 degrees to the x direction, then finally a y polarizer.

a) What is the probability that the photon makes it through the first (x) polarizer and what is the photon’s polarization after it comes through the first polarizer?

b) For a photon that got through the first (x) polarizer, what is the probability that that photon goes through the next two polarizers and what is the photon’s polarization after it comes through the last polarizer?

c) If the middle (25 degree) polarizer is removed, what is the probability that the photon gets through both (remaining) polarizers?

Answer 1

a)

When an unplarized light passes through a polarizer, its intensity reduces to half.

That is

(where is the initial intensity.)

Thus the probability that the photon makes it through the first (x) polarizer is

The polarization after it comes through the first polarizer is along x-xis.

b)

The second polarizer has its transmission axis rotated by relative to the axis of the first polarizer (x-axis).

Then the intensity of the photon after going through the second polarizer

The intensity of the photon after going through the third polarizer which is a y polarizer

  

Thus the probability that the photon makes through the last polarizer is

The light will be y-polarized.

c)

If the middle (25 degree) polarizer is removed, the probability that the photon gets through both (remaining) polarizers will be zero.