Video Transcript
The diagram represents red, green,
and blue light being deviated through an angle 𝛼 by a prism. Which of the following correctly
describes how 𝜆, the wavelength of the light, relates to the angle 𝛼? (A) As 𝜆 increases, 𝛼
increases. (B) As 𝜆 increases, 𝛼
decreases. (C) 𝜆 and 𝛼 are unrelated.
Okay, so since this question asks
us about the wavelength of different colors of light, let’s start by recalling which
of the colors in the question — red, green, and blue — has the longest and shortest
wavelength. Out of all the colors of visible
light, we know that red has the longest wavelength. This means that for red light, we
can say that the wavelength 𝜆 is large. Out of all the colors in the
diagram, blue light has the shortest wavelength. So we can say that for blue light,
𝜆 is small. The final color in the diagram,
green light, has a wavelength which is somewhere in between red and blue. This means that as the color of
light changes from blue to green to red, the wavelength 𝜆 increases.
So now that we know how the
wavelength changes for these different colors of light, let’s take a look at how the
angle of deviation 𝛼 changes for these different colors. The angle of deviation 𝛼 is this
angle shown here. And it measures the change in
direction of the light from when it enters the prism here to when it exits the prism
here. If we look carefully at the angles
shown here in the diagram, we can see that the angle of deviation for red light is
the smallest. And the angle of deviation for
green light is slightly bigger. And the angle is bigger again for
blue light. We can make this clearer for
ourselves by extending the dashed line that represents the direction the light was
traveling when it entered the prism like this.
We can then draw on the angles of
deviation for the different colors of light. And it’s easier to see that the
angle of deviation for red light shown here is smaller than the angle of deviation
for the blue light shown here. And we can also see that the angle
of deviation for the green light is somewhere in between these two angles. When we do this, we’re really just
reproducing what’s already in the diagram here. But because it’s so much bigger,
it’s easier to see the differences in the angles of deviation, which are called
𝛼.
So we’ve seen that red light has
the smallest angle of deviation, and blue light has the largest angle of
deviation. So if we again think about changing
the color of light from blue to green to red, we now know that the angle of
deviation 𝛼 decreases. And this gives us our final answer
to this question. We’ve seen that as the wavelength
𝜆 increases, the angle of deviation 𝛼 decreases, so our final answer is (B).
