Video Transcript
Which of the lines on the graph shows how the pressure exerted by radiation being reflected by a surface varies with the intensity of the radiation?
On the horizontal axis of our graph, we see the intensity of incoming radiation. And on the vertical axis, we see the pressure created by that radiation on a surface. Radiation pressure is a real phenomenon. And we can be helped in understanding it by thinking of radiation in terms of particles, photons. When a photon with some amount of momentum is incident on a surface and then, if the surface is reflective, is sent backward, then all that change in momentum experienced by the photon will create a force and therefore a pressure on the surface. That pressure is called radiation pressure. And in our diagram, we see a number of curves purporting to show the relationship between radiation pressure and radiation intensity.
To give an idea for radiation intensity, if we were to increase the number of photons per unit time that reach our surface, then that would be an increase in radiation intensity. There’s a mathematical relationship between radiation pressure and intensity that we can recall.
Before we do though, let’s see if we can narrow down our list of answer options. Thinking about the intensity of incoming radiation, if that intensity dropped all the way down to zero so that there was no incident radiation, then with no photons being incident on our surface, we know that no force, and therefore no pressure, could be created on that surface. This tells us that whichever of our curves is correct, it must pass through the origin; where intensity is zero, pressure must also be zero. We see then that we can eliminate the purple curve here as well as the black curve here. Both of these curves support the idea of nonzero pressure at zero intensity. Eliminating those options leaves us with the blue curve here, the orange line right here, and then the green curve here. All three of these curves do pass through the origin.
To see which of these three curves is correct, we can recall the relationship between radiation pressure and intensity for a perfectly reflective surface. That relationship says that radiation pressure 𝑃 is equal to two times radiation intensity 𝐼 divided by the speed of light in vacuum 𝑐. Notice that both the two and the 𝑐 are constant values. And so we can say that radiation pressure is directly proportional to radiation intensity. That means, for example, that if we were to double the radiation intensity, then we would double the pressure created by that radiation. Or if we were to triple the intensity, we would triple the pressure, and so on.
Graphically, if we were to double our radiation intensity, say taking that intensity from an initial value here to a final value here, then our equation tells us we must also double the radiation pressure. There’s only one of our remaining options which when we double the radiation intensity results in a doubling of the radiation pressure. That, we see, is the orange curve, the straight line.
For our answer then, we say that it’s the orange line that shows how pressure exerted by radiation being reflected by a surface varies with the intensity of that radiation.
