I have read this question:
Where John Rennie says:
Does the wavelength of the light matter?
No
Now in the same question, another answer, by DavePhd says:
Does the wavelength of the light matter?
Yes, shorter wavelength photons have higher momentum. p=h/λ
If I'm floating in space and I turn on a flashlight, will I accelerate?
Even these two have contradictory answers about the wavelength dependence of radiation pressure.
There is this question too, but none of the answers talk about my specific question:
How can a red light photon be different from a blue light photon?
Now there are many questions on this site about solar sails and radiation pressure, and the momentum of classical light and individual photons. The only thing these agree about is that classical light and even individual photons do have momentum, and they do exert pressure on the surface of the solar sail. Some of them agree on the fact that this happens via:
-
scattering (elastic or inelastic), this makes up most of the momentum transfer
-
absorption, this only relates to a small number of photons, but they do transfer momentum to the sail too
Radiation pressure is the mechanical pressure exerted upon any surface due to the exchange of momentum between the object and the electromagnetic field. This includes the momentum of light or electromagnetic radiation of any wavelength that is absorbed, reflected, or otherwise emitted
https://en.wikipedia.org/wiki/Radiation_pressure#Pressures_of_absorption_and_reflection
Now what none of them specifically describe, or agree on, is whether this is wavelength dependent, and how for example a higher energy photon (blue) would push the sail more then a lower energy photon (red).
The confusion comes from the agreed fact that only part of the momentum of the photons is transferred, and whether a higher energy photon should transfer more (relatively to a lower energy photon) momentum is questionable because of the different answers.
Questions:
-
Is radiation pressure wavelength dependent
-
does a blue photon move the solar sail more then a red photon?
Best Answer
They are both right. On a "per photon" basis, a 100% reflected photon (with $ k = 2\pi/\lambda$) imparts a momentum change of:
$$ \Delta p = -(p_f - p_i) = -(\hbar(-k) - \hbar k)=2\hbar k$$
which clearly depends on wavelength.
Meanwhile, given an energy ($E$) per area per time, the momentum transfer is:
$$ \Delta p = 2E/c $$
which doesn't depend on wavelength.