An _optical cavity_ or an _optical resonator_ is an optical element that, when ideal, confines a perfectly [standing light waves](Standing%20Electromagnetic%20wave) between two or more [mirrors](Mirrors.md).
# Two mirror cavities
Here we examine cavities constructed with only two mirrors.
## [Paraxial](Paraxial%20approximation.md) analysis
Using the fact that we may model a [model a mirror as a lens](Modeling%20mirrors%20as%20lenses.md) we may construct a model for an optical cavity in terms of a sequence of lenses shown below.
Here we have a sequence of lenses with alternating focal lengths $f_1$ and $f_2$ modeling a pair of circular mirrors acting as the walls of the cavity. Here we are also reminded how the focal lengths of the hypothetical lenses relate to the radii of curvature of the pair of mirrors.
### ABCD matrix
If we start by modeling the system as simply a pair of lenses we express this using a single ABCD matrix.The corresponding [ABCD matrix](Ray%20transfer%20matrix.md) for a pair of mirrors modeling the cavity system is given as
$M=\begin{pmatrix} 1-\frac{d_2}{f_1} & d_1+d_2-\frac{d_1d_2}{f_1}\\
\frac{-1}{f_1}-\frac{1}{f_2}+\frac{d_2}{f_1f_2} & 1-\frac{d_1}{f_1}-\frac{d_2}{f_2}-\frac{d_1}{f_2}+\frac{d_1d_2}{f_1f_2}
\end{pmatrix}$
where for the cavity sequence $d=d_1=d_2$ the matrix reduces to
$M=\begin{pmatrix} 1-\frac{d}{f_1} & 2d-\frac{d^2}{f_1}\\
\frac{-1}{f_1}-\frac{1}{f_2}+\frac{d}{f_1f_2} & 1-\frac{d}{f_1}-\frac{2d}{f_2}+\frac{d^2}{f_1f_2}
\end{pmatrix}$
#### Modeling a cavity as an ABCD matrix with n optical elements
In practice light traverses back and forth between the two mirrors some high number of times, $n.$ Thus we may want to calculate how the cavity functions as $n$ optical elements in terms of an ABCD matrix.
Thus, for $n$ pairs of mirrors representing $n$ times a light beam traverses the inside of the cavity, we obtain the [periodic ABCD matrix result](Ray%20transfer%20matrix.md#Sylvester's%20matrix%20theorem) 
# Cavities with more than 2 mirrors
* [ring resonators](Ring%20resonator.md)
# Uses of optical cavities
A [Laser cavity](Laser%20cavity) is an optical cavity with some medium placed between the mirrors.
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