A typical introduction to geometrical optics treats plane and spherical mirrors. At first glance, it may be surprising that texts seldom mention the cylindrical mirror, except for the occasional reference to use in fun houses and to viewing anamorphic art.1,2 However, even a cursory treatment reveals its complexity. Holzberlein used an extended object to qualitatively illustrate that images are produced both before and behind a concave cylindrical mirror.3 He also speculated on how this extreme astigmatism results in an observer's dizziness. By considering a simple point object, we make a more detailed analysis of the cylindrical mirror and the dizziness it induces. First, we illustrate how rays from a point object reflect to form not one point image but two line images. Next, we describe how an observer perceives a likeness of the object. Finally, we suggest how confusing depth cues induce dizziness. Although we focus on the concave cylindrical mirror, the discussion is easy to generalize to the convex cylindrical mirror.

Topics
Geometrical optics, Chemical elements, Diseases and conditions
1.
See, for example, Thomas D. Rossing and Christopher J. Chiaverina, Light Science: Physics and the Visual Arts (Springer, New York, 1999), pp. 52–53 and pp. 60–62.
2.
McLoughlin Bros., The Magic Mirror: An Antique Optical Toy (Dover Publications, New York, 1979). This book of anamorphic pictures comes with a flexible mirror that can be formed into a cylinder.
3.
Thomas M.
Holzberlein
, “
How to become dizzy with Derman's optical puzzle
,”
Phys. Teach.
20
,
401
–
402
(Sept.
1982
).
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4.
Since the cross section is circular, not parabolic, this only holds for paraxial rays.
5.
Frank J. Pedrotti and Leno S. Pedrotti, Introduction to Optics, 2nd ed. (Prentice Hall, Upper Saddle River, NJ, 1993), pp. 98–100.
6.
See EPAPS Document E-PHTEAH-43-012502.
This document may be retrieved via the EPAPS homepage (http://www.aip.org/pubservs/epaps.html) or from ftp.aip.org in the directory/epaps/in the phys_teach folder. See the EPAPS homepage for more information.
7.
E. H. Lockwood, A Book of Curves (Cambridge University Press, Cambridge, 1967), pp. 45–51.
8.
Samuel
Derman
, “
An optical puzzle that will make your head spin
,”
Phys. Teach.
19
,
395
(Sept.
1981
).
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Crossref
Search ADS
 
9.
Alan J.
DeWeerd
and
S. Eric
Hill
, “
Reflections on handedness
,”
Phys. Teach.
42
,
275
–
279
(May
2004
).
Google Scholar
Crossref
Search ADS
 
10.
David Falk, Dieter Brill, and David Stork, Seeing the Light: Optics in Nature, Photography, Color, Vision, and Holography (Wiley, New York, 1986), pp. 207–209.
11.
This can be demonstrated by modeling the lens and retina with a converging lens in front of a sheet of paper. A small light bulb shielded so that it only shines toward the cylindrical mirror approximates a point object.
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© 2005 American Association of Physics Teachers.
2005
American Association of Physics Teachers

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