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Chapter 6 Optics 6.1 The bending of light For the refraction at a surface holds: n i sin( θ i )= n t sin( θ t ) where n is the refractive index of the material. Snell’s law is: n 2 n 1 = λ 1 λ 2 = v 1 v 2 If Δ n 1 , the change in phase of the light is Δ ϕ =0 , if Δ n> 1 holds: Δ ϕ = π . The refraction of light in a material is caused by scattering from atoms. This is described by: n 2 =1+ n e e 2 ε 0 m ± j f j ω 2 0 ,j - ω 2 - i δω where n e is the electron density and f j the oscillator strength , for which holds: j f j =1 . From this follows that v g = c/ (1 + ( n e e 2 / 2 ε 0 m ω 2 )) . From this the equation of Cauchy can be derived: n = a 0 + a 1 / λ 2 . More general, it is possible to expand n as: n = n ± k =0 a k λ 2 k . For an electromagnetic wave in general holds: n = ε r μ r . The path, followed by a light ray in material can be found from Fermat’s principle : δ 2 ² 1 dt = δ 2 ² 1 n ( s ) c ds =0 δ 2 ² 1 n ( s ) ds =0 6.2 Paraxial geometrical optics
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Unformatted text preview: 6.2.1 Lenses The Gaussian lens formula can be deduced from Fermats principle with the approximations cos = 1 and sin = . For the refraction at a spherical surface with radius R holds: n 1 v-n 2 b = n 1-n 2 R where | v | is the distance of the object and | b | the distance of the image. Applying this twice results in: 1 f = ( n l-1) 1 R 2-1 R 1 where n l is the refractive index of the lens, f is the focal length and R 1 and R 2 are the curvature radii of both surfaces. For a double concave lens holds R 1 < , R 2 > , for a double convex lens holds R 1 > and R 2 < . Further holds: 1 f = 1 v-1 b...
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