Light is obliquely incident on a perfectly absorbing screen at an angle \( \theta \) relative to the surface normal. Steps 1-7 should be carried out for two different polarizations of the wave: (a) \( \mathbf{B} \) field parallel to the surface, and (b) \( \mathbf{E} \) field parallel to the surface. Then proceed to step 8.
- Choose axis \( z \) normal to the surface and another axis parallel to (a) \( \mathbf{B} \) or (b) \( \mathbf{E} \).
- Write down the Maxwell stress tensor as a matrix (all components).
- Which component gives the radiation pressure?
- Express the pressure in terms of the energy density of the radiation.
- Is there a momentum transfer parallel to the surface? Find it or argue why it is absent.
- Write down the full Maxwell stress tensor in the reference frame where the axis \( z' \) is parallel to the wavevector of the incident wave.
- Rationalize the result of the previous step.
- What if the incident light is unpolarized?
- Use general properties of tensors to find the radiation pressure from the result of item #6. (Use a rotation matrix.) Compare with the result of item #4 (they should match).
- Give a physical interpretation of the angular dependence of the radiation pressure.
- How do the above results (both pressure and transverse momentum transfer) change if the surface is perfectly reflecting instead of absorbing?
- A plane wave is incident on a perfectly reflecting sphere of radius \( R \). Find the total radiation force acting on the sphere. (You will need to set up an integral over the illuminated half of the sphere.)
- Answer the same question for a perfectly absorbing sphere.