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26 Physics Formulary by ir. J.C.A. Wevers 6.3 Matrix methods A light ray can be described by a vector ( n α ,y ) with α the angle with the optical axis and y the distance to the optical axis. The change of a light ray interacting with an optical system can be obtained using a matrix multiplication: ± n 2 α 2 y 2 ² = M ± n 1 α 1 y 1 ² where Tr( M )=1 . M is a product of elementary matrices. These are: 1. Transfer along length l : M R = ± 10 l/n 1 ² 2. Refraction at a surface with dioptric power D : M T = ± 1 - D 01 ² 6.4 Aberrations Lenses usually do not give a perfect image. Some causes are: 1. Chromatic aberration is caused by the fact that n = n ( λ ) . This can be partially corrected with a lens which is composed of more lenses with different functions n i ( λ ) . Using N lenses makes it possible to obtain the same f for N wavelengths. 2. Spherical aberration is caused by second-order effects which are usually ignored; a spherical surface does not make a perfect lens. Incomming rays far from the optical axis will more bent.
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