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OPTI502
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
11) 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.
12) Determine the equation of rotation about the zaxis for a planoconvex 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 zcoordinate 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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 Fall '08
 Greivenkamp

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