I was watching a video on solar sails and it described how the momentum of the individual photons striking the sail is planck's constant divided by the wavelength of the photon. Does this mean that photons reflecting off of any object attenuate over time, increasing their wavelength with each reflection, or is something else happening?
In a frame where the mirror is moving toward the light source, the interaction will slow the mirror. Some of the mirror's kinetic energy and momentum are given to the reflected photon and the reflected photon has greater energy/shorter wavelength than the incoming photon.
In a frame where the mirror is moving away from the light source, the interaction will increase the speed of the mirror. This time the mirror gains energy and the reflected photon leaves with a longer wavelength than before.
There will be a frame where the initial and final speed of the mirror are identical. In that frame, the photon has the same energy/wavelength before and after the reflection.
It seems to me that the mirror is either moving towards the source, away from the source, or is stationary with respect to the source. For a given initial condition is it possible to find one frame in which they approach each other and another in which they move apart?
The motion of the source is irrelevant. All we care about is whether the "push" from the light makes the mirror go faster or go slower. And that only depends on the motion of the mirror.
Assume the light comes from the left and strikes a mirror on the right. If the mirror is moving right (in our frame), then it will gain energy and the photon will lose energy. If the mirror is moving left (in our frame) then the mirror will lose energy and the photon will gain energy.
It's really the same thing as throwing a tennis ball so it strikes a moving train. Whether it speeds up or slows down has nothing to do with your motion, just the train's. If the train is approaching you, the ball will reflect with higher speed (higher energy). If the train is receding, the ball will reflect with less speed (lower energy).
Solar sails are a method for spacecraft propulsion, using radiation pressure exerted by sunlight on mirrors.
Radiation pressure is the pressure exerted by the EM field, on the surface due to the exchange of momentum.
Solar radiation exerts pressure on the sail due to reflection and a small portion of photons is absorbed.
The momentum of the photon is p=E/c. The momentum of the photon depends on the wavelength p = h/λ.
An ideal sail has 100% specular reflection that is elastic scattering. An actual sail will have 90%.
Due to the law of conservation of momentum, any change in the total momentum of the waves or photons must involve an equal and opposite change in the momentum of the matter it interacted with (Newton's third law of motion), as is illustrated in the accompanying figure for the case of light being perfectly reflected by a surface. This transfer of momentum is the general explanation for what we term radiation pressure.
Now you are asking whether the photon will lose momentum every time it interacts with a mirror.
The radiation pressure again can be seen as the transfer of each photon's momentum to the opaque surface, plus the momentum due to a (possible) recoil photon for a (partially) reflecting surface. Since an incident wave of irradiance If over an area A has a power of IfA, this implies a flux of If/Ep photons per second per unit area striking the surface. Combining this with the above expression for the momentum of a single photon, results in the same relationships between irradiance and radiation pressure described above using classical electromagnetics. And again, reflected or otherwise emitted photons will contribute to the net radiation pressure identically.
The answer is yes, the photon will transfer some of its momentum to the mirror, thus, the wavelength of the photon will change.