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Question Video: Comparing Component Waves for Different Intensity against Wavelength Curves Physics

The graph shows how the output power of three laser-light sources varies with the wavelength of the light that they emit. The laser-light sources emit most strongly at one peak wavelength, with the output decreasing as the wavelength varies from the peak wavelength. Diagrams I and II represent groups of waves emitted from two of the light sources. Diagram II represents the waves emitted by the light source that produced the blue-colored spectral distribution curve on the graph. What is the color of the curve that would correspond to the waves represented by diagram I?

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Video Transcript

The graph shows how the output power of three laser-light sources varies with the wavelength of the light that they emit. The laser-light sources emit most strongly at one peak wavelength, with the output decreasing as the wavelength varies from the peak wavelength. Diagrams I and II represent groups of waves emitted from two of the light sources. Diagram II represents the waves emitted by the light source that produced the blue-colored spectral distribution curve on the graph. What is the color of the curve that would correspond to the waves represented by diagram I?

In this question, we’ve been given a graph that shows the intensity of the light emitted by three laser sources. The red curve represents the source with the greatest power output, the green curve represents the curve with the lowest power output, and the blue curve represents the source that is in between. We are also given groups of waves emitted by two of the light sources. We know group II corresponds to the light source shown by the blue curve on the graph. And we need to work out which source group I corresponds to, the source corresponding to the green line or the source corresponding to the red line.

We can work out the answer to this question by comparing the intensity of light produced by the two groups of waves. If group I produces a higher intensity of laser light than group II, then we know that it must correspond to the source represented by the red curve. If group I produces a lower intensity of laser light than group II, then we know that it must correspond to the source represented by the green curve. To start, let’s remind ourselves about some of the properties of laser light.

A perfect laser would produce light that is completely coherent. This means that all the waves emitted from the laser had the exact same wavelength, and each wave would have the same shape or wave form. Additionally, to get high-intensity laser light, we would require each of these waves to be in phase, peaks lining up with peaks and troughs lining up with troughs. This is an example of a group of coherent light waves. All the waves have the same wavelength and wave form. They also happen to be in phase.

If a laser produces perfectly coherent light where each wave is in phase with the others, then the laser will have a very high intensity. This is because light waves interfere with each other and produce a resultant wave. If the initial light waves are perfectly in phase with each other and coherent, then the resultant wave has the greatest possible amplitude.

For example, imagine two coherent waves that are perfectly in phase with each other, and each have an amplitude of 𝐴. They will interfere with each other to produce a resultant wave of amplitude two 𝐴. If, however, the two initial waves are slightly out of phase with each other, the resultant wave will have a smaller amplitude. This leads to a lower intensity of light. Importantly, this can happen if the waves are coherent but slightly out of phase, and it will definitely be the case if the waves are not coherent in the first place.

In real lasers, the light emitted is not perfectly coherent. A laser will produce light with a small range of wavelengths, meaning that not all the waves can be in phase with each other all the time. The intensity of the laser depends on how out of phase these waves are. The further away the waves are from being coherent, the lower the peak intensity of the laser. Let’s apply this idea to the groups of waves given to us in this question.

We’ll start by looking at group II, which we know corresponds to the light source represented by the blue curve on the graph, the light source with middling intensity. If we look closely, we can see that these waves all have different wavelengths. For example, the wavelength of this red wave at the top is shorter than the wavelength of this black wave at the bottom. This means that these waves are not perfectly in phase.

Let’s compare the position of the peaks of each wave at this point here. The peak of the red wave is on this dotted line, but the peaks of the other waves get increasingly further away. By the time we reach the black line, we actually get a trough. We can see that this light is not perfectly coherent. Let’s now repeat this process for group I. Again, we can see that the waves all have different wavelengths, and the peaks of each wave do not line up. So again, this light is not coherent.

But let’s now compare the two diagrams. Just by looking at the waves, it’s much easier to tell that group I isn’t coherent than it is for group II. The difference in the wavelengths of the waves is much larger, and the difference in phase between the waves is much more pronounced. In other words, the waves in group I are even less coherent than the waves in group II. Because group I is much further away from being coherent than group II, this set of waves must correspond to a less intense laser.

Going back to our graph, we see that the green line represents a laser with a lower peak intensity than the blue line. So, this must be our answer. The green curve must correspond to the waves represented by diagram I.

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