Radiation pressure can be simply understood in terms of electromagnetic wave phenomena without delving into special relativity or introducing photons. We simply recall that A. electromagnetic waves consist of transverse electric and magnetic fields, perpendicular to each other and the direction of wave propagation and B. surfaces are made of protons and electrons. B. isn't necessary, but it helps me visualize it.
|An electromagnetic wave approaches an object made of free protons and electrons. The wave I found on google images, it apparently comes from someone named Amanda McPherson at University of Alaska.|
Consider the wave hitting the surface. What does the electric field do? It makes the protons and electrons accelerate in or opposite its direction, in the plane of the surface, giving them a velocity. The electrons, being 1800 times less massive, will end up moving a lot faster*.
|The electric field (red arrows) makes the protons move slowly in its direction, and the electrons move quickly in the opposite direction.|
Then, what does the magnetic field do? If the particles are stationary, it does nothing, but since the electric field set them in motion, the magnetic field couples to their velocity and provides a force. The force is perpendicular to the magnetic field, and perpendicular to the direction of motion (which was the direction of the electric field, perpendicular to the magnetic field), meaning that it creates a force in the direction of wave propagation, making the electrons move in that direction, driving the whole object forward.
|The magnetic field (blue arrows) couples with the velocity of the electrons, and changes their direction towards that of the wave propagation. I have neglected the force on the protons, because their velocity is so much slower.|
So there you have it. An electromagnetic wave hits a surface, the electric field sets the electrons in motion in the plane of that surface, the magnetic field couples to that motion and forces them in the direction of the wave, causing a force on the entire object. Thus, radiation pressure arises.
|My Ph.D. is in physics, not graphic design.|
There are a few space probes that have solar sails that use this principle for propulsion, including the Japanese probe IKAROS (whyyy would they call it that?!). I think one of the best descriptions of some of the additional nuances is this old xkcd blag post on the subject.
*This makes the most sense if the surface is metal, so that the electrons are unbound to the nuclei.