In many cases we approximate light as rays pointing along the direction in which the wave propagates. In doing so we model light beams as being exactly parallel to the propagation direction, hence we refer to light in _ray optics_ as being subject to the _paraxial approximation_. Rays can't be used to model [[diffraction]], however, they reveal how light rays are concentrated (i.e. focused) in a system and thus this is a useful approximation for many situations. # Linear Approximations In modeling light propagation as rays, we need to linearize our physical model. Thus, * The incidence on an optical element (such as a [lens](Lens.md) or [mirrors](Mirrors.md)) is modeled as being normal to the device. Thus for a small $\theta$ made by a ray with respect to an optical axis, $\sin{\theta}\cong\theta$ and $\tan{\theta}\cong\theta,$ linearizing the trigonometric functions for small angles and making $\theta$ equivalent to the slope of the ray. * The rays themselves are modeled as two component [vectors](Linear%20Algebra%20and%20Matrix%20Theory%20(index).md#Vectors), $\begin{pmatrix}x\\x'\end{pmatrix}$, where $x$ is the distance of a ray from the optical axis at a [principal plane](Principal%20plane.md) and $x'$ is its angle. * The propagation of light through space or optical elements is modeled in terms of [linear transformation](Linear%20map.md)s referred to as [ray transfer matrices](Ray%20transfer%20matrix.md). # Snell's Law In accordance with the [linear paraxial approximations](Paraxial%20approximation.md#Linear%20Approximations) [Snell's law](Optics%20(Index).md#Snell's%20law) reduces to $n_1\theta_1=n_2\theta_2.$ # Fresnel approximation A version of the [paraxial approximation](Paraxial%20approximation.md) applied to propagating [electromagnetic wave](Electromagnetic%20wave.md)s is the so called [Fresnel approximation](Fresnel%20approximation.md). #Electromagnetism/Optics