502 Homework 2010 Set 1

502 Homework 2010 Set 1 - OPTI-502 Optical Design and...

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OPTI-502 Optical Design and Instrumentation I John E. Greivenkamp Homework Set 1 Fall, 2010 Assigned: 8/24/10 Lecture 1 Due: 8/31/10 Lecture 3 1-1) Use Fermat’s principle to determine the shape (equation) of a concave mirror in air that produces a perfect image of a distant (at infinity) point source a distance f to the left of the mirror vertex. Remember that for an imaging situation, the optical path lengths (OPLs) for all rays connecting the object and image points are equal. Since rays from infinity are parallel, a reference plane at an arbitrary z can be used to measure the OPL. 1-2) Determine the equation of rotation about the z-axis for a plano-convex lens in air with thickness t and index n that will bring all incident rays parallel to its axis to a common focus at the point (1,0). The equation of rotation z = f(y) gives the z-coordinate or sag of the surface along an arc on the surface. This arc is rotated about the optical axis to produce the rotationally symmetric lens surface. Derive the exact analytic form of this curve.

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