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How do waves reflect off of surfaces? How do we account for the images that we see reflected in various objects? Discover the answers to these questions as we investigate the rays and angles defining the law of reflection.

The Reflection of Waves

When I was little, I liked to look at reflections of myself. I would make goofy faces in the mirror or dance around in front of a car window. I thought it was really fun to see how surfaces could reflect my childish antics. But the first time I saw my reflection in a spoon, I was amazed. Looking at the spoon’s inner surface, I saw my image reflected both upside down and backwards.

Back then, I didn’t understand why the reflection of my face appeared that way, but now I know that the image I saw was the result of basic principles that govern the reflection of waves.

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The incident ray is red and the reflective ray is blue in this diagram.
Incident Reflective Rays Diagram

Incident and Reflected Rays

Wave reflection always works the same way, whether the wave is a light wave, a sound wave, or a water wave. It describes a change in the direction of a wave when it strikes a surface. In talking about reflection and some other wave properties, it’s helpful to think of a wave as a ray, a straight line through space that indicates the path of a wave.

For example, we know that a light wave from the sun travels in a straight line toward the Earth. Because it’s an electromagnetic wave, we could think of it as having the typical wavelike up-and-down shape. But we can also think of it like a straight-line ray. A ray of sunlight is an appropriate concept for how we should think of waves in reflection.

So from now on, in this lesson, we’ll refer to all our waves as ‘rays.’Think about a single ray of sunlight. The ray that initially comes down from the sun is called the incident ray. This is really the term we use for any ray that approaches a reflective surface. The Earth isn’t the best example for reflection, so let’s say that we’ve got a mirror here instead.

The incident ray comes in and strikes the mirror at a certain angle. Then, it bounces off the mirror and proceeds in another direction. The ray that travels away from the reflective surface is called the reflected ray.

Incident and reflected rays are related to one another in that the angle of the reflected ray matches that of the incident ray.

A ball bouncing off of a pool table illustrates the law of reflection.
Law of Reflection in Pool

To visualize this, think about a typical pool table.

Say you’re playing a game of pool, and you’re trying to get the 5 ball into this side pocket. You’d have to hit the ball at an angle so that it would bounce off the opposite rail and roll into the pocket. If the ball hits the rail at too shallow an angle, it will end up too far to the left. If the ball hits the rail at too wide an angle, it will end up too far to the right. The ball will always bounce off the rail so that the angle at which it approaches the rail equals the angle at which it bounces off the rail. This principle is known as the law of reflection.

The Law of Reflection

The law of reflection tells us in very clear terms the relationship between the angles of our incident and reflected rays.

To define these angles, we first identify the normal : the imaginary line that is perpendicular to the reflective surface. When the incident ray strikes the surface, it creates an angle with the normal, which we call the angle of incidence. The angle of incidence measures the position of the incident ray in relation to the normal. Notice that the angle of incidence is not the angle between the incident ray and the surface. It’s the angle between the incident ray and the normal.

The incident and reflected angles are the same, according to the law of reflection.
A curved surface contains multiple normals that reflect rays in different directions.
Normals on Curved Reflective Surface

If you look at your own reflection on the inside of a spoon, you’ll end up seeing an image that is upside down and backwards.

The incident rays from the top of your head will be reflected towards the bottom. The incident rays from your chin will be reflected towards the top. Because the spoon is curved from top to bottom, your reflection appears upside down. But the spoon is also curved from one side to the other.

So incident rays from one side of your face are reflected on the other side. Try it and see! You can stick out your tongue on the left side, and you’ll see it reflected on the right. The law of reflection explains why we see the images that we do in all types of reflective surfaces.

Lesson Summary

The reflection of waves describes a change in the direction of waves when they strike a surface. We refer to these waves in terms of the incident ray that strikes a surface, and the reflected ray that bounces off a surface. Perpendicular to this surface is the imaginary normal, a line which we use to measure the angle of incidence and the angle of reflection.

According to the law of reflection, the wave’s angle of reflection is equal to the wave’s angle of incidence. This law applies to curved surfaces as well as those that are flat or straight. Because the law applies throughout a curved surface as the normal line varies, we can see strange, distorted reflections in curved objects, like funhouse mirrors and silver spoons.

Learning Outcomes

Once you have completed this lesson, you should be able to:

  • Define incident ray, reflected ray, angle of incidence, and angle of reflection
  • Summarize the law of reflection
  • Describe how a wave is reflected on flat surfaces and curved surfaces
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