A ball lens is a type of thick [biconvex lens](Biconvex%20lens.md) where the radii of curvature are $R_1=R_2=R$ and typically it is in the shape of a full sphere. # Paraxial model Shown below is a diagram of a ball lens with input rays in the [[paraxial approximation]]. The gray vertical line indicates the focal plane. The fact that the paraxial rays do not converge at a single clear focal point is indicative of severe [[spherical abberation]]s in this model.  The image adopted from the [RP Photons encyclopedia](https://www.rp-photonics.com/ball_lenses.html) ## ABCD matrix The form of the [ray transfer matrix](Ray%20transfer%20matrix.md) follows directly from the [ABCD matrix](Biconvex%20lens.md#ABCD%20matrix) for a [biconvex lens](Biconvex%20lens.md). here we set $d=2R,$ since that's the distance traversed through a sphere. Thus $M=\begin{pmatrix}-1 & 2\frac{n_1}{n_2}\\ \frac{2(n_1-n_2)}{n_2R} & 2\frac{n_1}{n_2}-1\end{pmatrix}$ #Electromagnetism/Optics #ExperimentalTools/ExperimentalToolsinOptics