Video Transcript
The diagram shows a point P that one of the three light rays A, B, and C might
possibly pass through after being reflected. Which light ray would pass through the point? (A) Ray A, (B) ray B, (C) ray C, (D) all of these rays.
The question is asking us to work out which of the three rays, A, B, or C, passes
through point P after reflecting off the surface shown in the diagram. Let’s recall that in the absence of anything in the way, light rays travel in
straight lines. We see though that, in this case, there is something in the way of these light
rays. Specifically, there’s this surface right here, which the light rays will reflect
off. We can see that this surface is not flat. Reflection off an uneven surface like this is known as diffuse reflection. We can recall that the law of reflection tells us what happens to light rays
reflecting off a surface.
First, we’ll consider a flat surface. We can draw in a line perpendicular to it, which is known as the normal line or the
normal to the surface. Let’s suppose that 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 ray will be reflected from the surface according to the law of reflection, which
says that 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, 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. Because the surface is uneven, the direction of the normal line will not be the same
at all points on the surface. In this case, for each incident light ray, we need to take care to draw in the normal
line in the direction perpendicular to the particular part of the surface that the
light ray hits.
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
ray A does pass through point P.
Now, we need to see whether or not rays B and C also pass through this point P. We’ll use the exact same process to find the path of the reflected rays as we just
used for ray A. Extending rays B and C until they meet the surface, drawing in the normal to the
surface at each point, and applying the law of reflection, we have the path of the
reflected rays for light rays B and C. Ray B ends up reflected such that it hits the surface again at this point, while ray
C ends up over here.
So, neither of the reflected rays B and C pass through point P. The only one that does is ray A. So, the correct answer here is given in option (A). The only light ray that passes through the point marked P is ray A.
