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=== Example: Thin lens ===
Consider a beam traveling through a thin lens with focal length ''f''. The ray transfer matrix is
<math display="block">\begin{bmatrix}A&B\\C&D\end{bmatrix}=\begin{bmatrix}1&0\\-1/f&1\end{bmatrix}.</math>
and so
<math display="block">q_2 =\frac{Aq_1+B}{Cq_1+D} = \frac{q_1}{-\frac{q_1}{f}+1} </math>
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