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Ch 9, Mirrors, Lenses
and Optical Systems
9.1
Geom
etr
ical
Opti
cs &
Pla
ne
Mir
rors
In this chapter the dimensions of the mirrors,
prisms and lenses discussed
are much greater than the
wavelength of light and
hence diffraction effects can
be ignored. In these circumstances light travels in
straight lines according to
the laws of reflection and
refraction, and so pathways
are accurately represented
with rays. These conditions
are called the conditions of
geometrical optics.
Ray Tra
cing
To investigate the images produced by
mirrors and lenses ray tracing can be
carried out. Using rays, known
pathways of light are modelled on a
scaled, two-dimensional diagram and
the characteristics of the resulting
image can be identified. The image can
then be fully described by its:
nature—Is the image real or virtual?
(discussed later)
orientation—Is the image upright or
inverted?
position—Where is the image in
relation to the mirror?
size (including magnification)—What is
the height of the image? By what factor
has the size of the image changed?
Images
in a
Pla
ne M
irro
rThe object and image are exactly the
same size. All images formed by plane
mirrors have the following characteristics:
The image is always upright.
The image is the same distance behind
the mirror as the object is in front.
The image is the same size as the
object.
Images in
a
Pla
ne M
irror
Use ray tracing to locate the
image of the pom-pom on the
top of this girl's hat, which is 50
cm from the mirror as shown.
9.1
Quest
ions
4, 7, 8, 9
9.2
Applica
tions o
f
Curve
d M
irrors:
Conca
ve M
irrors
All curved mirrors are either
concave or convex. A
concave mirror is curved
like the inside of the bowl of
a spoon, whereas a convex
mirror is shaped like the
back of a spoon. (One way
to remember which is which
is to recall that a concave
mirror forms a small cave or
may cave in.)
Watch
Concave Mirrors
Ray D
iagra
ms
Particular conventions apply to the construction of a
ray diagram (Figure 9.12).
A vertical line called the optical axis represents
the reflecting surface, i.e. the back of the mirror.
Although the mirror surface is curved, the optical
axis is a straight vertical line. A ray diagram tends
to use a much larger vertical scale than horizontal
scale, thus allowing the mirror to be represented
by a straight line with little loss of accuracy.
The optical axis is perpendicular to the principal
axis, and the pole, P, is placed at the intersection
between the optical axis and the principal axis. A
small curved mirror symbol is placed here to
indicate the type of mirror being used.
The principal focus of the mirror, F, and its centre
of curvature, C, are located on the principal axis
to scale.
Traditionally, the object is on the left of the optical
axis, along with the eye that will view the image.
The object is usually represented as a small
vertical arrow.
Ray Diagrams: Concave Mirror
Conca
ve M
irro
r R
ay
Traci
ng
Ray Diagram
Examples
Summary of Images formed by Concave Mirrors
Magnifi
catio
n
Exa
mple
A man stands in front
of his shaving mirror
and is disappointed with the image he sees. The focal length
of the concave mirror
is 50 cm, and he is standing 1.5 m from
its pole. Use a ray diagram to explain what he sees in the mirror.
9.2
Questio
ns3, 4, 5, 6, 9
9.3
Conve
x M
irro
rs
Convex M
irror
Ray Tra
cing
Conve
x M
irro
r R
ay
Traci
ng
Images fo
rmed
by C
onvex
Mirro
rAll images are
upright, virtual and
diminished. As the
object is brought
closer to the
mirror, the image
increases in size,
but it will never be
the same size as
the object.
Exa
mple
A shop uses a convex
mirror of focal length
2.0 m for security purposes. If a person
1.5 m tall is standing
4.0 m from the mirror,
describe the nature of
the image seen. What
is the magnification of
the image?
Mirro
r Form
ula
The mirror formula provides
the relationship between the
focal length of a mirror, f, the
distance of the object from
the pole of the mirror, u, and
the distance of the image
from the pole of the mirror, v.
The relationship is:
Mir
ror
Form
ula
Exa
mple
A person stands 30 cm
from the pole of a concave mirror and an
inverted image is formed 60 cm from the mirror. What is the
focal length of the mirror?
9.3
Questio
ns2, 9