Video: Eg17S1-Physics-Q17

Compare laser light, X-rays from a Coolidge tube.

04:34

Video Transcript

Compare laser light, X-rays from a Coolidge tube. Point of comparison coherence of the emitted light.

When it comes to this point of comparison, there is really a yes or no response to it. Light is either coherent or it’s not. So for both of these cases, for laser light as well as X-rays produced from a Coolidge tube, we want to answer whether this light is coherent.

Let’s start by considering the light emitted by a laser. The word laser is an acronym. It stands for light amplification by stimulated emission of radiation. We’ll find that the key to answering this question about the coherence of laser light is contained in this acronym. In particular, it’s the process of stimulated emission that helps to determine laser lights coherence. Say that we have an electron and this electron has a special property that has an elevated energy level. It’s not at the ground state energy level, which it could occupy, but rather is in an excited state. It’s possible though overtime for this electron to drop back down to the ground state. This can happen in two different ways.

One is through a spontaneous process, one that simply happens at a given time without any energy input from the outside. But another way this transition can happen is when the transition is stimulated by some outside energy. In particular, a photon which has just the right amount of energy to interact with the electron and lead to this transition. As the electron drops from a higher to a lower energy level, something interesting happens. The electron emits a photon which is essentially identical to the photon which encountered the electron in the first place. These two photons had the same direction at the same frequency and, critically, the same phase. Having the same phase means that the peaks of one wave align with the peaks of the other wave and the troughs of one wave align with the troughs of the other.

These two photons then, one of which caused this emission and one was the result of the emission, are practically identical to one another. And, of course, these two photons are now available to do something similar, a repeat process, with other excited electrons. And after that process, there’re even more photons moving in the same direction at the same frequency and in phase with one another. There is another way of naming this property of being in phase. And that’s to say that these waves are coherent. If we added them together, they would add with perfectly constructive interference. The high points of each wave line up with the high points of every other wave. And the same with the low points, the troughs.

This in-phase relationship between emitted photons occurs because those photons are stimulated to be emitted by other identical photons. When it comes then to the emission of laser light, we can say that this light is coherent radiation. Each photon is in phase with every other photon. That’s the story with laser light.

Now, what about X-rays produced by a Coolidge tube? To figure this out, let’s recall just how a Coolidge tube is constructed. A Coolidge tube is made of an evacuated glass chamber with a cathode and an anode inside that chamber. At the end of the cathode, there’s a small filament typically made of tungsten. When the filament gets very hot, on the order of thousands of degrees Celsius, electrons boil off the filament and are drawn towards the anode by a potential difference set up between cathode and anode. Because the electrons are emitted from a tungsten filament, that means that this current of electrons are not in phase with one another. They’re not coherent as they leave the filament.

The same thing is true of light emitted from an everyday incandescent light bulb. The bulb probably has a tungsten filament. And the photons that come from that filament are out of phase with one another. They’re incoherent. In the same way, so are the electrons in this beam. Over the gap between cathode and anode, these electrons build up tremendous speeds accelerated, as we mentioned, by a potential difference. When they do reach the anode, the target material, they crash into it with significant kinetic energy. The electrons lose most of their energy in this collision process. And that energy is then emitted as X-rays from the Coolidge tube.

Because the electrons in this current are already out of phase with one another, being emitted as they are from a tungsten filament, that tells us that the X-rays produced by these colliding electrons are also out of phase one with another. And we know that another name for out-of-phase light is incoherent light. And so, we can say that these X-rays themselves are incoherent. They don’t have a constant phase relationship with one another. And that has to do with the way they were generated by electrons which themselves were incoherent. This then is how we would compare the coherence of laser light to that of X-rays from a Coolidge tube.

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