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By Wevers J.C.A.

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The change of a light ray interacting with an optical system can be obtained using a matrix multiplication: n1 α1 n2 α2 =M y2 y1 where Tr(M ) = 1. M is a product of elementary matrices. These are: 1. Transfer along length l: MR = 1 0 l/n 1 2. 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 ni (λ). Using N lenses makes it possible to obtain the same f for N wavelengths.

4 The uncertainty principle If the uncertainty ∆A in A is defined as: (∆A)2 = ψ|Aop − A |2 ψ = A2 − A 2 it follows: ∆A · ∆B ≥ 12 | ψ|[A, B]|ψ | ¯ , and because [x, px ] = i¯h holds: ∆px · ∆x ≥ 12 h ¯ , and ∆Lx · ∆Ly ≥ 12 h ¯ Lz . 5 The Schr¨odinger equation The momentum operator is given by: pop = −i¯h∇. The position operator is: xop = i¯h∇p . The energy h∂/∂t. The Hamiltonian of a particle with mass m, potential energy U and total operator is given by: Eop = i¯ energy E is given by: H = p2 /2m + U .

This angle is called Brewster’s angle. The situation with r = 0 is not possible. 6 Polarization The polarization is defined as: P = Ip Imax − Imin = Ip + Iu Imax + Imin where the intensity of the polarized light is given by Ip and the intensity of the unpolarized light is given by Iu . Imax and Imin are the maximum and minimum intensities when the light passes a polarizer. If polarized light passes through a polarizer Malus law applies: I(θ) = I(0) cos2 (θ) where θ is the angle of the polarizer.

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