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MIT2_71S09_practice3

# MIT2_71S09_practice3 - 2.71/2.710 Optics Practice Exam 3...

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2.71/2.710 Optics Practice Exam 3 Spring ‘09 1. A thin bi-convex lens with the same absolute curvature on both faces is used in the two imaging systems shown below. In the first, both object and image are in air, whereas in the second the object is “immersed” in a material of index n 0 < n g , where n g is the index of the glass used to make the lens. Compare the two imaging systems in terms of imaging condition and magnification. 2. In the configuration below, lenses L1 and L2 are identical with focal length f , and we consider them to have infinite aperture. The system is illuminated coherently by an on-axis plane wave. 1

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(a) Write an expression for the field at x in terms of the thin complex transparencies g 1 , g 2 . (b) Consider the specific case with f = 10cm and g 1 , g 2 defined as: If λ = 1 µ m, derive and sketch the intensity at the output plane x . 3. Example: OTF of the Zernicke phase mask The thin phase transparency whose schematic is given below is placed at the Fourier plane of a unit magnification telescope with focal length f = 10cm. What is the optical transfer function for quasi-monochromatic illumination at wavelength λ = 1 µ m? 4. Goodman, Problem 6-10 5. Calculate and sketch the Fourier transform F ( u ) of the function x 2 πx 2 πx �� f ( x ) = sinc cos + cos b Λ 1 Λ 2 2
Assume that the following condition holds: 1 1 1 1 1 , , b Λ 1 Λ 2 Λ 1 Λ 2 6. A very large

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