Question Video: Calculating the Path of Light Rays Undergoing Specular Reflection Physics • Second Year of Secondary School

Video Transcript

Specular reflection involves light rays reflecting from an even surface, as shown in the diagram. The diagram shows four points — 𝐷, 𝐸, 𝐹, and 𝐺 — that the three light rays 𝐴, 𝐵, and 𝐶 might possibly pass through after being reflected. Which of the points would the light ray 𝐴 pass through?

In this first part of the question, we’re asked to consider the light ray labeled 𝐴 and to work out which of these four points — 𝐷, 𝐸, 𝐹, or 𝐺 — that light ray will pass through after being reflected from this surface. We’re 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 let’s 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. We’ll label this angle of incidence as 𝜃 𝑖.

When the light ray gets reflected from the surface, this reflected ray makes an angle to the normal known as the angle of reflection. We’ll label this angle of reflection as 𝜃 𝑟. 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 𝜃 𝑖 and the angle of reflection is 𝜃 𝑟, then the law of reflection says that 𝜃 𝑖 is equal to 𝜃 𝑟.

In this part of the question, we’re asked to consider what happens to light ray 𝐴. So we’re gonna start off by extending light ray 𝐴 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 𝐴, 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 let’s draw in the normal to the surface at the point where the light ray 𝐴 meets it. The angle of incidence, 𝜃 𝑖, 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 it’s 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 we’ve 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 𝐸. And so our answer to this first part of the question is that the light ray 𝐴 will pass through point 𝐸.

Okay, now let’s look at the second part of the question.

Which of the points would the light ray 𝐵 pass through?

This second part of the question is asking us to do the same thing we just did for light ray 𝐴 but now for the light ray labeled 𝐵. The process is gonna be exactly the same as what we just did for light ray 𝐴. So we’ll extend light ray 𝐵 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 we’ll appeal to the law of reflection in order to tell us the direction of the reflected ray. Extending light ray 𝐵, 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 𝜃 𝑖. 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 𝐷. So our answer to the second part of the question is that the light ray 𝐵 will pass through point 𝐷.

Finally, let’s look at the third part of the question.

Which of the points would the light ray 𝐶 pass through?

So now we’re gonna do the same thing again but this time for light ray 𝐶. First, we’ll extend light ray 𝐶 up until the point where it meets the surface. We find that the ray meets the surface at this point here. Now let’s draw in the normal to the surface at this point. We can add the angle of incidence of light ray 𝐶 to our diagram. Measuring this angle, we find that it’s approximately equal to 55 degrees. So let’s 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 𝐺. So our answer to this final part of the question is that the light ray 𝐶 passes through point 𝐺.