Reflection

Laws of reflection

To discuss the laws of reflection, we need a set-up (see the figure below). For a reflection, we need a reflection surface and an incoming ray of light, and we will automatically have a reflected ray of light that has a different direction than the incoming ray. The reflection surface has a perpendicular line through it called the normal, the incoming (or incident) ray makes an angle of incidence${\theta }_i$with the normal, and the reflected ray makes an angle of reflection${\theta }_r$with the normal. The laws of reflection are:

1. The incoming ray, the reflected ray, and the normal to the reflection surface are all in the same plane;
2. The angle of incidence is the same as the angle of reflection:${\theta }_i={\theta }_r$;
3. The reflected ray is on the other side of the normal than the incoming ray.

Laws 1 and 3 are pretty intuitive and you may not need to remember them explicitly, but law 2 is important to remember. The laws are nicely illustrated in the figure below.

This 2-dimensional (because of the first law) diagram of reflection illustrates the second and third laws of reflection. A ray of light starts at P, is reflected at O and travels towards Q, Wikimedia Commons CC BY-SA 3.0.

Being able to draw rays of light that reflect off of surfaces is important. These drawings are called ray diagrams. The figure above is an example of a ray diagram.

Types and causes of light reflection

There are two main types of light reflection, and their causes have to do with the reflection surface being smooth or rough.

Specular reflection

A mirror and still water are good examples of smooth reflection surfaces. The smoothness of the reflection surface means that the normal to the reflection surface stays the same (in the case of flat reflection surfaces, or plane mirrors) or changes slowly and gradually (in the case of curved surfaces, which we will not go into further in this article) from place to place on the reflection surface. The laws of reflection now say that, because the normal is the same everywhere on the reflection surface, the reflected light from one ray of incoming light will all have the same direction.

This allows for virtual images, which are images of (real) objects that appear to be somewhere that they are not. The reason for this false appearance is that the light that reaches our eyes comes from a direction that is not the direction of the object. See the figure for an illustration. The information that the eye receives will tell it that the object at point A, say an apple, is somewhere behind the mirror (because our brains assume that the light has always travelled in a straight line), while in reality, the apple is in front of the mirror, next to the eye.

The eye sees the apple that is at place A through a plane mirror. The direction of the reflected light makes the eye think that the apple is at place A', so it sees a virtual image, Wikimedia Commons.

Diffuse reflection

Most regular things have a rough surface: bread, walls, trees, et cetera. The rough surface means that the normal to the reflection surface changes wildly between different places on the surface. The laws of reflection now say that, because the normal is so different, the direction of the reflected ray of light is also different from place to place: the reflected light gets diffused into different directions. See the figure below for an illustration of this effect. This also means that there is no such thing as a mirror image in the case of rough reflection surfaces.

In (a), we see diffuse reflection: the reflected light has different directions. In (b), we see specular reflection: the reflected light has one direction and travels as one ray, Wikimedia Commons CC BY-SA 4.0.

Examples of reflections

Seeing yourself in your bathroom mirror (which is a plane mirror that causes specular reflection) is an everyday example of a reflection of light. Another example of reflections is the diffuse reflection most objects produce, and how these determine what colour we perceive an object to be.

This way, the reflection of light largely determines what colours objects are: red objects will absorb less of the red frequencies than of the other frequencies, etc. However, not only light but all waves can be reflected.

One example is sound waves: they can reflect off tunnel or cave walls and come back to you, making you hear a reverb or echo. Another sound reflection effect most of us have experienced is that sound sometimes appears to come from the side of you where there is a wall, while the sound producer is clearly to your opposite side. The last example of sound reflection is bats using echolocation: they produce a sound themselves and then listen to the echoes produced by the reflection off of walls to figure out where those walls are.

Water waves can also be reflected. When water waves hit a wall, a part of them will be absorbed and the other part will be reflected. The reflections of waves other than light are determined by the same laws of reflection that we talked about earlier!

Importance of light reflection

The reflection of light has been vital for a big part of life on Earth. Most things do not naturally emit visible light, so we can only see them because they reflect the light of the Sun towards our eyes (remember that most things are rough, so there will always be a part of the reflected rays that reaches our eyes). Thus, without light reflection, animals would be blind to everything except the Sun and other things that produce visible light on their own.

Additionally, different materials reflect, transmit, and absorb different colours of light in different quantities. This makes the reflected sunlight coloured. This colour gives animals information about the possible materials that an object is made of.