The Paraxial Approximation: Revisited

  • V. V. Ivchenko Department of Natural Sciences Training, Kherson State Maritime Academy, Kherson 73000, Ukraine


We define the paraxial ray as the ray making infinitesimal angles with a central axis and normal to a reflecting or refracting surface. We show that for some physical situations these conditions can be relaxed, while for others non-compliance with one of them can lead to major deviations in the behavior of the output light beam. We first derive and analyze the generalized spherical mirror formula. Next, we consider the case of refracting ball and show that there can occur the situation, where the parallel input light beam is split into converging and diverging output beams in it. The issues outlined in this article will be useful for students, when learning the basics of geometrical optics.

Dec 13, 2020
How to Cite
IVCHENKO, V. V.. The Paraxial Approximation: Revisited. Revista Cubana de Física, [S.l.], v. 37, n. 2, p. 84-87, dec. 2020. ISSN 2224-7939. Available at: <>. Date accessed: 18 july 2024.
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