Question Video: Calculating the Path of Light Rays Undergoing Specular Reflection Physics • 9th Grade

Specular reflection involves light rays reflecting from an even surface as shown in the diagram. 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 points would the light ray A pass through? Which of the points would the light ray B pass through? Which of the points would the light ray C pass through?

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Video Transcript

Specular reflection involves light rays reflecting from an even surface as shown in the diagram. 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 points would the light ray A pass through?

This question shows us a diagram containing three light rays. And in this first part of the question, we are asked to consider the ray labeled A. Our task is to work out which of these three points, D, E, and F, the light ray A will pass through after it gets reflected from the surface. The question tells us that we have specular reflection, which means the light rays are reflecting from an even surface. Sure enough, looking 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. Let’s suppose that we have some even surface like this. At any point on that surface, we can draw a dashed line which is perpendicular to it. That is, it meets it 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 coming in like this. We can define the angle of incidence of this light ray as the angle between the 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 with the normal that’s called the angle of reflection. We’ll label this angle of reflection as 𝜃 𝑟.

The law of reflection tells us that whenever a light ray gets reflected in this way, the angle of incidence must equal the angle of reflection. For an angle of incidence 𝜃 𝑖 and an angle of reflection 𝜃 𝑟, the law of reflection says that 𝜃 𝑖 is equal to 𝜃 𝑟. We can use this information to work out what happens to the light ray A in the question. We’ll start by extending the light ray A up until the point where it meets the surface. We can recall that in the absence of anything in its way, a light ray travels in a straight line. So extending light ray A, we find that it meets the surface at this point here.

We want to work out the angle that this ray gets reflected at. And to find this, we can use the law of reflection. But first, we’re going to need to work out the angle of incidence. So let’s add 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 the incident ray and the normal. In this case, if we measure the angle of incidence, we find that it’s equal to 45 degrees.

The law of reflection then tells us that the angle of reflection will be equal to this angle of incidence. This means that to find the direction that the light ray A gets reflected in, we need to measure this same angle 45 degrees on the opposite side of the normal. Once we have measured the angle, we can then draw in the path of the reflected ray. Extending this reflected ray shows that it passes through the point labeled F. So our answer to this first part of the question is that the light ray A will pass through point F.

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 this time for the light ray labeled B. The process is going to be exactly the same. So we’ll begin by extending light ray B up until it meets the surface. We’ll then add in the normal at this point. We can now measure the angle of incidence between light ray B and this normal. We find that just as for light ray A, this angle is 45 degrees. Then, appealing to the law of reflection, we know that the angle of reflection will also be equal to 45 degrees.

Measuring this 45-degree angle of reflection on the opposite side of the normal and extending the reflected ray, we find that it passes through the point marked E. So our answer to this second part of the question is that the light ray B will pass through point E.

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 going to do the same thing again, but this time for light ray C. So we’ll extend light ray C until it meets the surface. And we’ll add in the normal at this point. Measuring the angle of incidence, we find that it’s again equal to 45 degrees. So let’s draw the reflected ray with the same angle on the opposite side of the normal. We find that when we extend this reflected ray, it passes through the point marked D. This means that our answer to this final part of the question is that the light ray C will pass through point D.