# What causes reflection?

Nov 28, 2016

Light is reflected when there is a mismatch between materials through which the light is travelling.

#### Explanation:

Light is reflected when there is a mismatch between materials through which the light is travelling. This can range from partial reflection, like a reflection from a lake surface or a window, to complete reflection, like a reflection from a mirror. The difference is in the amount of mismatch between the materials.

The property of the material we are interested in is called the Index of Refraction, and is usually denoted by the letter $n$. The index of refraction is the ratio of the speed of light in vacuum to the speed of light in the material of interest. Since nothing travels faster than light in a vacuum (including light in a material) this is always a value greater than $1$. Here are some examples of indices of refraction:

Normally the index of refraction is used to determine the angle that light propagates in a material when it "bends" or refracts, but we can also use it to calculate how much light reflects.

We use Fresnel's equations to do this calculation, after having used Snells's Law to calculate the angle of refraction.

The simplest version of this calculation is when light is propagating directly at the interface (called normal incidence where ${\theta}_{i} = 0$) in which case the reflection coefficient is given by

$R = {\left[\frac{{n}_{2} - {n}_{1}}{{n}_{2} + {n}_{1}}\right]}^{2}$

It is clear from this that the higher the difference between the materials, the more light that will be reflected.