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MIT2_71S09_ups7

# MIT2_71S09_ups7 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY 2.71 Optics Spring ’09 Problem Set #7 Posted Monday, Apr. 13, 2009 — Due Wednesday, Apr. 22, 2009 1. Zernicke phase mask. You are given an imaging system which consists of two thin transparencies T1, T2 and two thin lenses L1, L2 arranged as shown in Figure A. The shapes and dimensions of T1, T2 are shown immediately below in Figure B. 1 f 1 f x x 2 f 2 f x T1 z T2 L2 L1 Figure A (not to scale) 10μm z 1μm glass, n =1.5 x air T1 z a =3cm glass, n =1.5 b =7cm 0.5μm T2 air opaque opaque x Figure B (not to scale) Transparency T1 is infinitely large in the x dimension. Lenses L1, L2 are identical, with infinitely large apertures and focal lengths f 1 = f 2 = 10cm. Numerical

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values for the symbols a , b denoting lateral feature sizes of T2 are defined in Figure B. The illumination is an on–axis plane wave at wavelength λ = 1 µ m. The obser- vation plane is located one focal distance behind L2. 1.a) What is the intensity immediately after T1? 1.b) What is the optical field immediately before T2? 1.c) What is the intensity measured at the observation plane?
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