Question

A wave plate is cut in such a way so the optical axis is in the plane of the plate. The wave plate causes a phase shift of Phi between the components parallel and perpendicular to the optical axis. This wave is now sandwiched between two polarizers crossed at 90 degrees. The optical axis of the plate is at 45 degrees to the axis of the polarizers.   (a) Find the transmittance (for beam irradiance) of the system when the incident beam is polarized parallel to the first polarizer.

(b) What is the transmittance when two polarizers are parallel

I know how to find irrandiance due to two polarizers, but is there a difference between irradiance and transmittance? and how does the wave plate affect it? Thanks!

Answer 1

First, I think talk about irradiance from polarizers is not correct, I would prefer transmittance, but for your problem, yes, transmittance and irradiance are the same.

When the beam pass through the first polarizer, it will have the polarization direction of the polarizer, now, the plate has 45 degrees about the original polarization.

What does the plate? Since you have two equals (in amplitude) components of polarization in reference to the optical axis of the plate (cos and sin of 45 are the same), you will have one component along the optical axis of the plate and other perpendicular to it. The parallel component will be shifted by pi respect to the perpendicular.

When the two components arrive to the second polarizer, they interfere (because this polarizer is, again, 45 degrees respect to the plate). What happens when two beams shifted pi each other? They interfere destructively, so the transmittance of the system is 0 (no light pas through that optical array).

If the second polarizer is parallel to the first, as before, plate is 45 degrees about each polarizer, so, you will have 0 transmittance too. Intermediate positions between 0 and 90 degrees between two polarizers will result in non-zero transmittances.

You can see how to work a DIC microscope