Question

A single photon from an unpolarized wave travelling 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 30 degrees to the x axis, then finally a y polarizer.

a. What is the probability that the photon makes it through the first (x) polarizer?

b. If it comes through the first polarizer, what is its polarization state in between the first two polarizers?

c. What is the probability that the initial photon makes it through the first two polarizers?

d. If it comes through the first two polarizers, what is its polarization state in between the second and third polarizers?

e. What is the probability that the initial photon makes it through all three polarizers?

f. If it comes through all three polarizers, what is its polarization state?

g. If it comes through all three polarizers, what was its polarization state in between the first and second polarizers?

h. Do the probabilities for all the possible outcomes add to 1?

Answer 1

a)

The intensity of an unpolarized light will be reduced by a factor of when passed through a polarizer. Thus if is the intensity of the unpolarized light, then will be the resultant intensity.

That is

Then the probability of photons coming out of the first polarizer is .

b)

When it comes through the first polarizer, the resultant wave become polarized along the x-direction.

c)

When the wave polarized along the x-axis passes through the second polarizer at to the x-axis, the intensity of the transmitted wave will be

Then the probability of transmission is .

d)

The polarization state of the resultant wave between the second and third polarizers is along the axis to the x-axis.

e)

It is given that the transmission axis of the third polarizer is y-axis. Thus it makes an angle of . Thus the transmitted intensity

Thus the probability of photon that transmits through all the three polarizers will be

f)

Its polarization state is along the y-axis.

g)

Same as in answer b.

h)

No