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.