Refraction

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.

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

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$90°$.

• 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.