# Refraction

Have you noticed how curved glass deforms the objects behind it? Or when in a pool, how the underwater part of someone's body looks squashed when you look at it from above the water? This all has to do with refraction. In this article, we will cover the refraction of light. We will define refraction, look at the laws governing refraction, and we will give an intuitive explanation for why it occurs.

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## The meaning of refraction

In principle, light travels in a straight line as long as there is no event to stop it from doing so. A change of materials, also called media, through which the light is travelling is such an event. Because light is a wave, it may be absorbed, transmitted, reflected, or a combination thereof. Refraction can take place at the boundary between two media, and we can define it as follows.

Refraction of light is the change in the direction of light once it passes the boundary between two media. This boundary is called the interface.

All waves undergo refraction at an interface of two media through which the wave travels at different speeds, but this article focuses on the refraction of light.

### Refractive index

Every material has a property called the refractive index, or index of refraction. This index of refraction is denoted by$n$, and it is given by the ratio of the speed of light in vacuum$c$and the speed of light in said material$v$:

$\mathrm{refractive}\mathrm{index}\mathrm{of}\mathrm{material}=\frac{\mathrm{speed}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{vacuum}}{\mathrm{speed}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{material}}$.

Thus, notated with symbols, the refractive index is defined by

$n=\frac{c}{v}$.

Light is always slower in any material than in a vacuum (because, intuitively, there is something in its way), so$n=1$for a vacuum and$n>1$for materials.

The refractive index of air can in practice be regarded as$1$, as it is about$1.0003$. The refractive index of water is about$1.3$, and that of glass is about$1.5$.

## Laws of refraction

To discuss the laws of refraction, we need a set-up (see the figure below). For refraction, we need an interface between two media with different refractive indices and an incoming ray of light, and we will automatically have a refracted ray of light that has a different direction than the incoming ray. The refractive index of the medium through which the incoming ray of light is travelling is${n}_{i}$, and that through which the refracted ray of light is travelling is${n}_{r}$. The interface has a perpendicular line through it called the normal, the incoming ray makes an angle of incidence${\theta }_{i}$with the normal, and the refracted ray makes an angle of refraction${\theta }_{r}$with the normal. The laws of refraction are:

• The incoming ray, the refracted ray, and the normal to the interface are all in the same plane.
• The relation between the angle of incidence and the angle of refraction is determined by the refractive indices of the media.
• The refracted ray is on the other side of the normal than the incoming ray.

The situation above is illustrated in the figure below.

The 2-dimensional (because of the first law) diagram of refraction illustrates the second and third laws of refraction qualitatively. Wikimedia Commons CC0 1.0

If a light ray goes from a certain refractive index to a higher refractive index, the angle of refraction is smaller than the angle of incidence. Thus, from the figure about refraction above, we can conclude that${n}_{r}>{n}_{i}$in that figure. It is important to be able to draw so-called ray diagrams qualitatively in the context of refraction: these are drawings of rays that undergo refraction.

Both refraction towards and away from the normal is displayed by this glass, first going to a higher and then to a lower refractive index

The exact relation between the angle of incidence and the angle of refraction is called Snell's law, and it is

${n}_{i}\mathrm{sin}\left({\theta }_{i}\right)={n}_{r}\mathrm{sin}\left({\theta }_{r}\right)$.

This law of refraction can actually be explained through a very simple principle, called Fermat's principle, which states that light always takes the path that costs the least time. You could compare this to a bolt of lightning always taking the path of least resistance to the ground. In the figure above, we concluded that light is faster in the left material than in the right material. Thus, to go from its starting point to its endpoint, it will want to stay in the left material for longer to benefit from its higher speed, and the light does this by making the contact point with the interface a bit higher up, and changing direction at that point: refraction happens. Making it too high would mean that the light makes a detour, which is not good either, so there is an optimal contact point with the interface. This contact point is exactly at the point where the angle of incidence and the angle of refraction are related as stated in the second law of refraction above.

## Refraction: Critical angle

If a light ray goes from a certain refractive index to a smaller refractive index, then the angle of refraction is larger than the angle of incidence. For some large angles of incidence, the angle of refraction is supposed to be larger than$90°$, which is impossible. For these angles, refraction does not take place, but only absorption and reflection occur. The largest angle of incidence for which there is still refraction is called the critical angle${\theta }_{\mathrm{c}}$. The angle of refraction for the critical angle of incidence is always a right angle, so$90°$.

One example of a critical angle in practice is if you are underwater and the water is still (so the air-water interface is smooth and flat). In this situation, we have (approximately)${n}_{i}=1.3$and${n}_{r}=1$, so light rays go from a certain refractive index to a smaller refractive index, so there is a critical angle. The critical angle turns out to be approximately$50°$. This means that if you don't look straight up but to the side, you will not be able to see above the water, because the only light that reaches your eyes is light that is reflected and comes from underwater. There is no refraction, but only reflection (and some absorption). See the illustration below for a schematic view of the critical angle in this situation, where the light comes from the water below and goes towards the interface with air.

This image shows the refraction of light as it leaves water (medium 1) and enters air (medium 2). The critical angle is represented in situation (3) where no refraction occurs and all light is reflected or absorbed, adapted from image by MikeRun CC BY-SA 4.0.

• Light travels at a different speed through different materials, which gives every material a certain refractive index given by $n=c/v$.
• If a light ray goes from a certain refractive index to a higher refractive index, the angle of refraction is smaller than the angle of incidence, and vice versa.
• There is a critical angle if you go from high refractive index to low refractive index, above which there is no refraction anymore, but only absorption and reflection.

## Refraction vs reflection

This definition looks a lot like the definition of reflection, but there are some big differences.

• In the case of a reflection, the ray of light stays in the same medium at all times: it hits the interface between the two media and then goes back into its original medium. In case of refraction, the ray of light passes the interface and continues into the other medium.
• The angle of reflection is always equal to the angle of incidence, but as we will see in the next section, the angle of refraction is not equal to the angle of incidence.

## Examples of refraction

It might be good to look at some examples of refraction in daily life.

### An example of refraction in daily life

Perhaps the most useful invention that is entirely based on refraction is the lens. Lenses make clever use of refraction by using the two interfaces (air to glass and glass to air) and are made such that light rays are redirected to the producer's wishes. Read more about lenses in the dedicated article.

Rainbows are a direct result of refraction. Different wavelengths of light (so different colours) are refracted differently ever so slightly, such that a ray of light splits into its constituent colours once it undergoes refraction. When sunlight hits raindrops, this split happens (because water has a refractive index of 1.3 but slightly different for different colours of light), and the result is a rainbow. See the figure below for what happens within such a rain droplet. A prism works the same way, but with glass.

Sunlight entering the prism, refracting differently for its different constituent colours, and producing a rainbow

## Refraction - Key takeaways

• Refraction of light is the change in the direction of light once it passes the interface between two media.
• Light travels at a different speed$v$through different media, which gives every material a certain refractive index given by$n=c/v$.
• Light refracts at the interface between two media with different refractive indices.
• If a light ray goes from a certain refractive index to a higher refractive index, the angle of refraction is smaller than the angle of incidence, and vice versa.
• There is a critical angle if you go from a high refractive index to a low refractive index, above which there is no refraction anymore, but only absorption and reflection.
• Lenses use refraction to redirect light rays.

#### Flashcards in Refraction 5

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What is refraction?

Refraction of light is the change in the direction of light once it passes the boundary between two materials.

What are the rules of refraction?

The rules of refraction state that the angle of incidence and the angle of refraction are related by Snell's law.

How to calculate refractive index?

You can calculate the refractive index of a material by dividing the speed of light in a vacuum by the speed of light in said material. This is the definition of the refractive index.

Why does refraction occur?

Refraction occurs because, according to Fermat's principle, light always takes the path of least time.

What are 5 examples of refraction?

Examples of phenomena caused by refraction are: distortion of underwater objects when viewed from above the water, how lenses work, distortion of objects viewed behind a glass of water, rainbows, adjusting your aim when spearfishing.

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