Video Transcript
The diagram shows three points D,
E, and F that the three light rays A, B, and C might possibly pass through after
being reflected. Which of the following correctly
relates the rays to the points that they would pass through? (A) Ray A and point D, ray B and
point E, ray C and point F. (B) Ray A and point F, ray B and
point E, ray C and point D. (C) Ray A and point E, ray B and
point D, ray C and point F.
The question asks us to find out
which of the three rays A, B, and C passes through which of the points D, E, and F
after reflecting off the surface shown in the diagram. Unless there is something in their
path, we know that light rays travel in straight lines. But, of course, in this case, there
is something in the way of these light rays. There’s this surface here, which
the light rays reflect from. We can notice that the surface is
not flat. Reflection off an uneven surface
like this is known as diffuse reflection. Let’s recall that the law of
reflection tells us what happens to light rays reflecting off a surface.
To begin with, we’ll consider a
flat surface. We can draw in a line perpendicular
to it. This line is known as the normal
line or the normal to the surface. Let’s now suppose we have an
incident light ray that makes an angle of 𝜃 sub 𝑖 to this normal line. This is the angle of incidence of
the light ray. The law of reflection says that
when this ray is reflected from the surface, the angle of reflection is equal to the
angle of incidence but on the opposite side of the normal. The angle of reflection, which
we’ll call 𝜃 sub 𝑟, is the angle that the reflected light ray makes to the normal
line, that is, this angle here. So, in terms of symbols, the law of
reflection says that 𝜃 sub 𝑖 is equal to 𝜃 sub 𝑟.
We have to be careful applying this
law when we have diffuse reflection from an uneven surface. In this case, for each incident
light ray, we need to draw in the normal line perpendicular to the particular part
of the surface that that light ray hits. Because the surface is uneven, the
direction of the normal will not be the same at all points on the surface.
Let’s now use this information to
extend the path of each of these three light rays from the question. We’ll begin with ray A. We know it travels in a straight
line until it meets the surface. Then we need to draw in the normal
line at the point where the ray hits the surface. That normal line looks like
this. We know from the law of reflection
that the angle between the normal and the reflected ray is equal to this angle here
between the incident ray and the normal. Measuring this angle and drawing in
the reflected ray at this same angle, we see that after being reflected, ray A
passes through point E.
Now let’s look at ray B. Extending the ray until it meets
the surface, drawing in the normal at this point, and applying the law of
reflection, we get the path of the reflected ray. We see that ray B passes through
point D.
Finally, we’ll consider ray C. Extending the ray’s path up to the
surface and drawing in the normal at this point, the law of reflection again tells
us the path of the reflected ray. We find that ray C passes through
point F.
We have found then that ray A
passes through point E, ray B passes through point D, and ray C passes through point
F. This matches the statement given in
option (C). Our answer then is option (C). The statement that correctly
relates the rays to the points that they would pass through after reflection is “Ray
A and point E, ray B and point D, ray C and point F.”
