Light of constant intensity is directed at a 100 percent reflective surface. The light strikes the surface at an angle, as shown in the diagram. If 𝜃 is less than 90 degrees, will the radiation pressure exerted by the light on the surface be greater than, less than, or equal to the radiation pressure when 𝜃 equals 90 degrees?
In our diagram, we see parallel rays of light being incident on a surface. The surface is oriented at an angle 𝜃 to these rays of light, and we see that 𝜃 is indeed less than 90 degrees. We want to compare the radiation pressure on the surface at an angle 𝜃 to the radiation pressure that would be on the same surface if the angle of 𝜃 equaled 90 degrees. We can understand this term radiation pressure a bit more easily by thinking of light not as a wave, but rather as a particle. If light is a particle, and we can call these particles photons, then parallel rays of light being incident onto a surface can be thought of as though we’re throwing lots and lots of, say, ping pong balls or tennis balls onto that surface.
Each collision that occurs when a photon reaches a surface and then bounces off of it, as it does in the case of an 100 percent reflective surface, helps to contribute to the overall radiation pressure of that light on the surface. The more particles there are that bounce off a surface in some amount of time, the greater the radiation pressure. Notice that when our rays of light and our surface are at 90 degrees to one another, as they are in the sketch, that creates the maximum surface area for light to impact and therefore to contribute to the radiation pressure. At the opposite extreme, if we rotated our surface by 90 degrees, the surface and the rays would be parallel and no light would land on the surface. Because there would be no particles bouncing off of the surface, the radiation pressure on it would be zero.
We see then that when a surface is oriented at 90 degrees to incoming rays of light, the radiation pressure on it is maximized. And when, on the other hand, it’s parallel to those incoming rays, the radiation pressure is minimized; it’s zero. This means if we think about a surface being oriented at an angle that’s less than 90 degrees to the incoming rays of light, the radiation pressure exerted by the light on that surface will be less than the radiation pressure when 𝜃 is 90 degrees. We’ve seen this from looking at our two limiting cases, when 𝜃 equals 90 degrees and when 𝜃 equals zero degrees.