The Law Of Reflection (Physics): What Is It & How Does It Work?

Seeing your reflection in the mirror is something so common that you might take it for granted, but there is a lot to consider just lurking under the surface.

The flat surface of the mirror in your bathroom might give a perfect reflection, but how do curved fun-house mirrors produce such bizarre distortions, making you seem ultra-tall or short and squat? How can each light ray bounce off the surface in such a perfect way as to create a clear image? Why can't you see a clear reflection from a rough surface?

These questions might be the sort of thing you'd imagine an over-zealous child might ask, but the physics of reflection, and in particular the law of reflection, explains many phenomena and is an important stepping stone to understanding more complex concepts like refraction and Snell's law.

When a light wave hits a surface, all or part of it will turn around sharply and reflect away from the surface again. For a smooth surface like a plane mirror, almost all of the light that hits it is reflected, and the resulting image is a clean, "specular" reflection. This is the form of reflection you'll be most familiar with, and undoubtedly what you'll think of when you picture a reflection.

However, specular reflection isn't the only type: There are also diffuse reflections of light. When parallel light rays end up hitting a rough surface, the individual light rays strike slightly different points and are reflected in different directions as a result of the irregularity of the rough surface. This is called a diffuse reflection because even though all of the light is still reflected, the light waves are scattered all around and don't form a single, crisp image.

In some cases, for example at the surface of a window, you'll notice a feint reflection that's much less clearly-defined than you would see at a mirror. This is because at such an interface, there is some traditional reflection, but also a substantial chance that the light will be transmitted through the window instead.

You need ​Snell's law​ to completely describe what happens to the light transmitted through the window (which gets ​refracted​), but the law of reflection still explains what happens to the reflected light even in this more complicated situation.

Before moving on to discuss the law of reflection, it's a good idea to learn the terminology used to describe situations like this.

First, the light on the way to the mirror or surface is referred to as the ​incident light ray​ or simply the incident light, and that light after the reflection is called the ​reflected light ray​.

The ​angle of incidence​ of the incident light ray is the angle it makes with the "normal line" for the surface at the point of incidence. "Normal" in this context means the line that extends perpendicularly out from the surface at that point, so a light ray striking a mirror head-on will have a 0 degree angle of incidence, while a perfectly diagonally-incident ray will have a 45 degree angle of incidence.

The ​angle of reflection​ is very similar to the angle of incidence, but as you may expect, describes the angle the reflected light ray makes with the normal line to the surface at the point of incidence. This is just the counterpart to the angle of incidence defined above.

It's also worth noting that a light ray is a slightly idealized way to describe light – you basically just think about it in terms of perfectly straight rays, whereas in reality it's a transverse wave and much more complicated to describe. However, to understand reflection, you don't need this level of detail – it's always good to simplify things when you can in physics!

The law of reflection states that for an incident ray of light, the angle of incidence will equal the angle of reflection. Put in simple terms, if a light ray approaches the reflective surface exactly perpendicular to the surface, it will be reflected straight back along the same line, but if it's not quite perpendicular, it will be reflected off to the other side of the perpendicular line by an equal amount.

Calling the angle of reflection ​θ​_r and the angle of incidence ​θ​_i, the law of reflection formula is simply:

\(θ_r = θ_i\)

So if you shine a laser pointer at your bathroom mirror at an angle of 45 degrees to the normal line (so exactly half way between being aligned with the face of the mirror and being perpendicular to it), then it will be reflected off at 45 degrees in the opposite direction.

Think about a pool player bouncing a ball off a flat section of the cushion, or a tennis player judging the angle the ball will bounce up after hitting the ground. Both of these situations aren't ​perfectly​ equal in terms of the angle of incidence and the bouncing angle (because some energy is lost in both cases), but in essence, light behaves in the same way.

The simplest example of the law of reflection is when you look into a plane mirror. Imagine you're looking down in a full length mirror at your feet, and think about where the light rays are actually traveling.

The light rays come from your feet up toward the mirror, at a certain angle of incidence. The law of reflection tells us that the angle it reflects at has to match the angle it was incident at, so it must strike the mirror around half way between your feet and the height of your eyes, and you can calculate this exactly with a bit of trigonometry.

You might have noticed some problems with reflections when you're trying to watch TV, and this is another example of the law of reflection in everyday life. The problem is that the TV is a smooth surface and it's effectively acting as a plane mirror for the sun or lamp-light that's ruining your picture.

Although there are many technological attempts to fix this, you can leverage the law of reflection and simply twist the TV to change the angle between the normal line to the screen and the incident light, thus moving the reflection out of your eye-line.

Fun-house mirrors are a little more complicated, but you can understand what's going on if you think about the ​shape​ of the surface of the mirror. Think about how the law of reflection would apply to a mirror that was slightly curved, so that the top and bottom protruded out, and the center was comparatively further back. How would your image change?

There are many example problems you can try with a basic understanding of what the law means, but one is especially interesting and should help you to get to grips with the key concepts.

Imagine two mirrors at a 90 degree angle to each other and meeting at one edge, as if they were forming half a square shape. If you shine a ray of light at these two mirrors, it will reflect off the first, then the second, and then reflect away from the mirrors. However, the angle it ultimately reflects back at is parallel to the angle of incidence.

Can you prove this? Imagine that the light is incident at 30° on the first mirror and then work through the path of the ray one step at a time and see what you get. If you do, what if it wasn't specifically 30°, and you just said it was incident at an angle ​φ​ instead – can you prove the same thing in general?