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