Introductory Physics Volume Two

8.10 Multi-Lens Optical Systems 173
Example
§ 8.9 Sign Conventions and Coordinates System
We have used the coordinates
(x o , y o ) for the object and the coordinates
(x i , y i ) for the image. The
direction of positive y is the same
for both coordinate systems. The
direction of positive x was opposite.
Light
In
A curved mirror is also a lens. The coordinate
sign convention, stated as follows,
covers both types of lenses.
• The x-axis of the object coordinate system
is in the opposite direction as the incoming
light.
• The x-axis of the image coordinate system
is in the same direction as the outgoing light.
y o
y i
Light
x o
x Out i
Transmitting Lens
Light
In
Light
Out
x o
x i
y o
y i
Reflecting Lens
A concave mirror (as shown) is a converging lens, while a convex
mirror is a diverging lens. The sign convention for focal lengths is the
same for mirrors.
§ 8.10 Multi-Lens Optical Systems
Most optical systems are composed of more than one lens. We do
not need more theory in order to work with a multi-lens system. The
light passes from one lens to the next in sequence. In order to do a
computation with a multi-lens system, we need only use the image of
one lens as the object of the next lens.
Suppose that you have a diverging lens, f = −12cm, followed by a
converging lens, f ′ = 16cm. The lenses are 20 cm apart. You place an
object that is 9cm tall at a distance of 24 cm from the diverging lens.
We can construct the final image as follows.
24 cm
20 cm
28 cm 37.3 cm
Mirror
Object 1
8cm
12cm
Image 1
Object 2
12cm
16cm
Or we could compute the final image from the thin lens equation. Given
f = −12cm and x o = 24cm we can compute
1
= 1 x i f − 1 1
=
x o −12cm − 1
24cm = − 3
24cm −→ x i = −8cm
16cm
Image 2