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Chapter 23: Mirrors and Lenses Topic Review
Book Title: College Physics
Printed By: Ashley Hartwyk (ashley.hartwyk@gmail.com)
© 2018 Cengage Learning, Cengage Learning
Topic Review
Summary
23.1Flat Mirrors
Images are formed where rays of light intersect or where they appear to originate. A real
image is formed when light intersects, or passes through, an image point. In a virtual
image, the light doesn’t pass through the image point, but appears to diverge from it (Fig.
23.32).
Figure 23.32
A geometric construction to locate the image of an object placed in front of a flat
mirror. Because the triangles
and
are identical,
and
.
The image formed by a flat mirror has the following properties:
1. The image is as far behind the mirror as the object is in front of it.
2. The image is unmagnified, virtual, and upright.
23.2Images Formed by Spherical Mirrors
The magnification
of a spherical mirror is defined as the ratio of the image height to
the object height , which is the negative of the ratio of the image distance to the object
distance :
[23.2]
The object distance and image distance for a spherical mirror of radius
the mirror equation:
are related by
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[23.6]
where
is the focal length of the mirror.
Equations 23.2 and 23.6 hold for both concave (Fig. 23.33) and convex mirrors (Fig. 23.34),
subject to the sign conventions given in Table 23.1.
Figure 23.33
(a) The image of a concave mirror is real and inverted when the object is outside
the focal point, i.e.
. The image is larger than the object when
, and
smaller than the object when
. (b) The image of a concave mirror is virtual,
upright, and larger than the object when
.
Figure 23.34
The image of a convex mirror is virtual, upright, and behind the mirror.
23.3Images Formed by Refraction
An image can be formed by refraction at a spherical surface of radius (Fig. 23.35). The
object and image distances for refraction from such a surface are related by
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[23.7]
The magnification of a refracting surface is
[23.8]
where the object is located in the medium with index of refraction
and the image is
formed in the medium with index of refraction . Equations 23.7 and 23.8 are subject to the
sign conventions of Table 23.2.
Figure 23.35
An image formed by refraction at a spherical surface. Rays making small angles
with the principal axis diverge from a point object at and pass through the image
point .
23.5Thin Lenses
The magnification of a thin lens is
[23.10]
The object and image distances of a thin lens are related by the thin-lens equation:
[23.11]
Equations 23.10 and 23.11 are subject to the sign conventions of Table 23.3. Figure 23.36
illustrates how to locate the image of the object of a thin lens using ray diagrams.
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Figure 23.36
Ray diagrams for locating the image of an object. (a) The object is outside the focal
point of a converging lens. (b) The object is inside the focal point of a converging
lens. (c) The object is outside the focal point of a diverging lens.
The focal length in air of a lens with index of refraction
equation:
is given by the lens-maker’s
[23.12]
where
and
are the radii of curvature of the front and back surfaces.
23.6Lens and Mirror Aberrations
Aberrations are responsible for the formation of imperfect images by lenses and mirrors.
Spherical aberration results from the focal points of light rays far from the principal axis of
a spherical lens or mirror being different from those of rays passing through the center.
Chromatic aberration arises because light rays of different wavelengths focus at different
points when refracted by a lens due to the index of refraction depending on wavelength.
Chapter 23: Mirrors and Lenses Topic Review
Book Title: College Physics
Printed By: Ashley Hartwyk (ashley.hartwyk@gmail.com)
© 2018 Cengage Learning, Cengage Learning
© 2021 Cengage Learning Inc. All rights reserved. No part of this work may by reproduced or used in any form or by any means graphic, electronic, or mechanical, or in any other manner - without the written permission of the copyright holder.
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