Question

Let's imagine we have Right Circularly Polarized Light propagating in the +z^

direction toward a perfectly reflecting mirror. Before reflection, the light has the electric field:

E⃗ (z)=E0cos(kz−ωt)x^+E0sin(kz−ωt)y^.

After reflection, it is well known that the reflected light will now be Left Circularly Polarized, but what will the expression be for the electric field? The light now travels in the −z^
direction.

The electric field for Left Circularly Polarized light is
E⃗ (z)=E0cos(kz−ωt)x^−E0sin(kz−ωt)y^,
but this does not take into account that the direction of propagation has changed.

What is the proper electric field expression after reflection, and why (i.e. how did you come up with the expression)?

Answer 1

The expression for the electric field after reflection is E⃗ (z) = E0cos(kz−ωt)x^−E0sin(kz−ωt)y^, taking into account both the change in polarization and the change in direction of propagation.

Step-by-step explanation:

The expression for the electric field after reflection can be obtained by considering the change in direction of propagation. Since the light now travels in the opposite direction (-z^), the signs of both the sine and cosine terms in the electric field expression need to be reversed. Therefore, the proper expression for the electric field after reflection is:

E⃗ (z) = E0cos(kz−ωt)x^−E0sin(kz−ωt)y^

This expression takes into account both the change in polarization (from right circularly polarized to left circularly polarized) and the change in direction of propagation. It is obtained by reversing the signs of both the sine and cosine terms in the original electric field expression.