The _principal planes_ of an optical system or single element can be understood roughly as being the planes (perpendicular to the optical axis) at which a light ray enters and exits an optical system. In every situation the principal planes must intersect the axis at _principal_ points at which the [indices of refraction](Index%20of%20refraction.md) are equal. However, the possible positions of the principle planes relative to the center-plane of an optical system are limited by the geometry of the optical system. We can solve for the position of the principle plane in terms of [ray transfer matrices](Ray%20transfer%20matrix.md). # ABCD Matrix between Principle Planes Depending on a system's configuration, the principal planes for a particular setup may be defined at distances in [free space](Free%20space%20light%20propagation.md#ABCD%20matrix), $L_1$ and $L_2$ relative to the boundaries at the start or end of an optical system where we solve for a desired _effective [focal length](Optics%20(Index).md#focal%20length)_, $f_{eff}$ such that the overall [ABCD matrix](Ray%20transfer%20matrix.md) is $\begin{pmatrix} 1 & L_2\\ 0 & 1 \end{pmatrix}\begin{pmatrix} A & B\\ C & D \end{pmatrix}\begin{pmatrix} 1 & L_1\\ 0 & 1 \end{pmatrix}=\begin{pmatrix} A+L_2C & L_1A+B+L_1L_2C+L_2D\\ C & L_1C+D \end{pmatrix}$ $=\begin{pmatrix} 1 & 0\\ -1/f_{eff} & 1 \end{pmatrix}.$ where naturally where $L_1=L_2=0$, $f_{eff}=f.$  # Examples * For a [Thin lens](Thin%20lens.md) the principal planes are both exactly at the lens position. * In some situation the principal plane may need to extend inside or outside of an optical element. #Electromagnetism/Optics