Properties of caustics produced by a conic lens: meridional rays

We derive simple formulas for the caustic produced by a positive convex-plano and plano-convex conic lens by considering a plane wave incident on the lens along the optical axis. By using these equations a paraxial approximation for the caustics are provided in both configurations. Also, by using these equations it is possible to obtain the third order coefficient of spherical aberration. Changing the parameters of the lens (refraction index, conic constant, radius of curvature, thickness of the lens, etc.) we can modify the shape of the caustic, furthermore there are cases where the spherical aberration changes from positive to negative when we vary exclusively the conic constant. A formula for the Principal Surface as a function of the height also is given. We believe that the method to obtain the caustic that we report is straightforward, obtaining a relationship between caustics, wavefronts, and measurements of the spherical aberrations.

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