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Reflection: Angle of Incidence and Curved Surfaces

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  • 0:05 The Reflection of Waves
  • 0:37 Incident and Reflected Rays
  • 2:34 The Law of Reflection
  • 3:48 Reflection off of…
  • 5:24 Lesson Summary
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Lesson Transcript
Instructor: April Koch

April teaches high school science and holds a master's degree in education.

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.

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.
Law of Reflection Diagram

Just like our incident ray makes an angle of incidence, our reflected ray makes an angle of reflection. This angle measures the position of the reflected ray in relation to the normal. According to the law of reflection, the angle of incidence is equal to the angle of reflection. That means that if our light ray hits a mirror with a 15-degree angle of incidence, it will reflect off the mirror with a 15-degree angle of reflection. If it strikes the mirror at 70 degrees, then it reflects off the mirror at 70 degrees. It's very similar to our example with the pool table. The angle at which a wave strikes a surface equals the angle at which it reflects off the surface.

Reflection Off of Curved Surfaces

The examples that we've seen so far have all involved surfaces that are flat. A regular mirror is flat, and the rails on a pool table are flat. But what if you have a curved surface, like a doorknob, a funhouse mirror, or the inside of a spoon? How do waves reflect off of surfaces that are curved?

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