26Physics Formulary by ir. J.C.A. Wevers6.3Matrix methodsA light ray can be described by a vector(nα,y)withαthe angle with the optical axis andythe distance tothe optical axis. The change of a light ray interacting with an optical system can be obtained using a matrixmultiplication:±n2α2y2²=M±n1α1y1²whereTr(M)=1.Mis a product of elementary matrices. These are:1. Transfer along lengthl:MR=±10l/n1²2. Refraction at a surface with dioptric powerD:MT=±1-D01²6.4AberrationsLenses usually do not give a perfect image. Some causes are:1.Chromatic aberrationis caused by the fact thatn=n(λ). This can be partially corrected with a lenswhich is composed of more lenses with different functionsni(λ). UsingNlenses makes it possible toobtain the samefforNwavelengths.2.Spherical aberrationis caused by second-order effects which are usually ignored; a spherical surfacedoes not make a perfect lens. Incomming rays far from the optical axis will more bent.
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