Abstract
It is generally supposed that thin systems, including refracting surfaces and thin lenses, have powers that are necessarily symmetric. In other words they have powers which can be represented assymmetric dioptric power matrices and in the familar spherocylindrical form used in optometry and ophthalmology. This paper shows that this is not correct and that it is indeed possible for a thin system to have a power that is not symmetric and which cannot be expressed in spherocylindrical form. Thin systems of asymmetric power are illustratedby means of a thin lens that is modelled with small prisms and is chosen to have a dioptric power ma-trix that is antisymmetric. Similar models can be devised for a thin system whose dioptric power matrix is any 2 2 × matrix. Thus any power, symmetric, asymmetric or antisymmetric, is possible for a thin system. In this sense our understanding of the power of thin systems is now complete.
Highlights
It is generally believed that it is not possible for a refracting surface, a thin lens or any other thin system to have a dioptric power that is asymmetric
This paper has shown how that can be the case for a thin system
It is possible to have a thin system whose dioptric power is not of the conventional kind, and that the power can be asymmetric. It is the fourth term in Equation 11 that is responsible for the asymmetry
Summary
It is generally believed that it is not possible for a refracting surface, a thin lens or any other thin system to have a dioptric power that is asymmetric. The purpose of this paper is to challenge that belief and describe thin systems which do, have asymmetric powers. Fick’s and Long’s generalization of Prentice’s equation for prismatic effect is used to model a thin lens of a particular asymmetric power. This shows that asymmetric powers are possible for thin systems in general. We show the effect of a thin lens of a particular asymmetric power on rays traversing it.
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