### Video Transcript

Specular reflection involves light rays reflecting from an even surface, as shown in the diagram. The diagram shows four points โ ๐ท, ๐ธ, ๐น, and ๐บ โ that the three light rays ๐ด, ๐ต, and ๐ถ might possibly pass through after being reflected. Which of the points would the light ray ๐ด pass through?

In this first part of the question, weโre asked to consider the light ray labeled ๐ด and to work out which of these four points โ ๐ท, ๐ธ, ๐น, or ๐บ โ that light ray will pass through after being reflected from this surface. Weโre told in the question that we have specular reflection, which means the light rays reflecting from an even surface. Sure enough, if we look at the diagram, we see that the surface is indeed even.

In order to answer this question, we need to recall what happens when a light ray gets reflected. Suppose that we have some even surface. We can draw a dashed line that is perpendicular to this surface. That is, it meets the surface at an angle of 90 degrees. This dashed line is referred to as the normal to the surface. Now letโs suppose that we have a ray of light which is incident on the surface. We can define the angle of incidence of this light ray as the angle between the incident ray and the normal to the surface. Weโll label this angle of incidence as ๐ ๐.

When the light ray gets reflected from the surface, this reflected ray makes an angle to the normal known as the angle of reflection. Weโll label this angle of reflection as ๐ ๐. The law of reflection tells us that when a light ray gets reflected in this way, the angle of incidence is equal to the angle of reflection. If the angle of incidence is ๐ ๐ and the angle of reflection is ๐ ๐, then the law of reflection says that ๐ ๐ is equal to ๐ ๐.

In this part of the question, weโre asked to consider what happens to light ray ๐ด. So weโre gonna start off by extending light ray ๐ด up until the point where it meets the surface. Remember that in the absence of any objects in its way, a light ray travels in a straight line. So extending light ray ๐ด, we see that it meets the surface at this point here. We want to know the angle at which this ray gets reflected. And to find this, we can use the law of reflection.

But first, we need to work out the angle of incidence. So letโs draw in the normal to the surface at the point where the light ray ๐ด meets it. The angle of incidence, ๐ ๐, is then the angle between this incident ray and the normal to the surface. In this case, if we measure this angle of incidence, we find that itโs approximately equal to 40 degrees. The law of reflection then tells us that the angle of reflection will be equal to this angle of incidence. This means to find the direction in which this ray gets reflected, we need to measure this same angle, approximately 40 degrees, on the opposite side of the normal.

Once weโve measured this angle, we can then draw in the path of this reflected ray. Extending this ray shows that it passes through the point marked ๐ธ. And so our answer to this first part of the question is that the light ray ๐ด will pass through point ๐ธ.

Okay, now letโs look at the second part of the question.

Which of the points would the light ray ๐ต pass through?

This second part of the question is asking us to do the same thing we just did for light ray ๐ด but now for the light ray labeled ๐ต. The process is gonna be exactly the same as what we just did for light ray ๐ด. So weโll extend light ray ๐ต up until it meets the surface and use the normal to the surface at this point in order to work out the angle of incidence. Then weโll appeal to the law of reflection in order to tell us the direction of the reflected ray. Extending light ray ๐ต, we see it meets the surface at this point here.

We can draw in the normal to the surface at this point and mark on our diagram the angle of incidence ๐ ๐. We can measure the angle of incidence as approximately 35 degrees. Then appealing to our law of reflection, we can draw the reflected ray with the angle of reflection also being 35 degrees. Extending this reflected ray, we see that it passes through the point marked ๐ท. So our answer to the second part of the question is that the light ray ๐ต will pass through point ๐ท.

Finally, letโs look at the third part of the question.

Which of the points would the light ray ๐ถ pass through?

So now weโre gonna do the same thing again but this time for light ray ๐ถ. First, weโll extend light ray ๐ถ up until the point where it meets the surface. We find that the ray meets the surface at this point here. Now letโs draw in the normal to the surface at this point. We can add the angle of incidence of light ray ๐ถ to our diagram. Measuring this angle, we find that itโs approximately equal to 55 degrees. So letโs draw the reflected ray with the same angle on the other side of the normal. Extending the reflected ray, we see that it passes through the point marked ๐บ. So our answer to this final part of the question is that the light ray ๐ถ passes through point ๐บ.