Optical Instruments: Mirrors and Lenses

hand_with_sphere.jpg (6081 bytes)

Title: Hand with Reflection Sphere (Self-Portrait in Spherical Mirror)

( M.C. Escher/ Cordon Art-Baarn-Holland. All rights reserved )
Copyright 1995-1999 World of Escher, Inc.  This picture has been used without permission.

M.C. Escher's drawing of his hand holding a reflecting sphere. The sphere reflects everything in the room on its surface. Can you determine which hand Escher was holding the sphere in. Read Esher's quote to find out.
Hint:  This picture is a lithograph and so the prints are reversed from the artists original drawing.

"The picture shows a spherical mirror, resting on a left hand.   But as a print is the reverse of the original drawing on stone, it was my right hand that you see depicted. (Being left-handed, I needed my left hand to make the drawing.)  Such a globe reflection collects almost one's whole surroundings in one disk-shaped image.  the whole room, four walls, the floor, and the ceiling, everything, albeit distorted, is compressed into that one small circle.  Your own head, or more exactly the point between your eyes, is the absolute center.  No matter how you turn or twist yourself, you can't get out of that central point.  You are immovably the focus, the unshakable core, of your world."  - M. C. Escher

Is Escher's statement about the point between the eyes always being at the center of the sphere accurate?  Considering the eye as a lens, how does this statement relate to the object and image in mirrors and lenses?

Previously Asked Questions

Q:    In what ways are satellite dishes similar to concave mirrors?  In what ways are they different?

A:    Both satellite dishes and concave mirrors have close to spherical shapes.  Their common purpose is to concentrate a parallel beam of rays into a focus.  The dissimilarity between satellite dishes and mirrors is related to the fact that satellite dishes receive and focus radio signals, while mirrors receive and focus visible light.  In fact, both radio signals and visible light are electromagnetic waves that differ only by frequency.

Q:    Why are mirrors used in large telescopes instead of lenses?

A:    It is easier to correct aberrations in mirrors by modifying the mirrors shapes, than to correct aberrations in lenses.

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Image:  the optical counterpart of an object produced by an optical device (as a lens or mirror) or an
electronic device

Real Image: an optical image formed of real foci. (like that on a movie screen)

Virtual Image: an image (as seen in a plane mirror) formed of points from which divergent rays (as of light) seem to emanate without actually doing so.


Image formation
p = object distance (always positive)
i = image distance  (positive = real image, negative  = virtual image)
f = focal length
r = radius of curvature
Spherical mirror  35-4.gif (230 bytes)
Plane mirror (spherical mirror for r goesto.gif (52 bytes) inf.gif (53 bytes) ) p = -i
Spherical refracting surface  35-8.gif (259 bytes)
Thin lens  35-9.gif (436 bytes)
Lateral magnification m m = - i / p
Magnitude of lateral magnification |m| |m| = imageheight / objectheight
Optical instruments
Simple magnifying lens 35-12.gif (201 bytes)
Compound microscope 35-14.gif (348 bytes)
Refracting telescope 35-15.gif (200 bytes)

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List of Topics

Measurements Electric Potential Magnetism Electrical Circuits (AC) Optical Instruments: Mirrors and Lenses
Electrostatics Capacitance Sources of Magnetic Fields Maxwell's Equations Interference
Electric Fields Current and Resistance Magnetism in Matter Electromagnetic Waves Diffraction
Electric Flux Electrical Circuits (DC) Electromagnetic Induction Interaction of Radiation with Matter: Reflection, Refraction, Polarization