PHYSICS EXPERIMENTS — 132
15-1
Experiment 15
Simple Lenses
In this experiment you investigate image
formation by simple optical lens systems. A lens is
a piece of transparent material shaped so that all
light rays hitting the lens from the same (object)
point end up going through the same (image) point
after being bent by passage through the lens. The
location of the image point depends on that of the
object point and on a property of the lens called the
focal length. You verify thin lens theory and
determine lens focal length.
Preliminaries.
Part A. Converging Lens.
Figure 1 is a schematic representation of the
formation of a real image by a converging lens.
Real images may be projected onto a screen. In this
experiment, only real images may be observed.
for a converging lens is positive. All other symbols
in these equations are positive as shown in Figure 1,
with the exception of y’, which is negative.
Part B. Diverging Lens.
A simple diverging lens does not produce a real
image. However, combining a known converging
lens with the unknown diverging lens may result in
a real image that can be projected on a screen. If the
two lenses are in contact, the lenses acting together
have an effective focal length feff given by:
1
1 1
(eq. 3)
 
f eff
f1 f 2
where f1 and f2 are the focal lengths of the
individual lenses in contact .

Procedure.
Part A. Converging Lens.
• Align the system components on the optical
bench. A backlit screen with an arrow is the object.
The image falls on white cardboard. Set the lens
between object and image screen and move the
image screen until a sharply focused image appears.
Record the object and image distances relative to
the lens.
Figure 1. Image Formation by a Thin Converging Lens
The theory for thin lenses gives the following:
M

1 1 1
 
s s' f
(eq. 1)
y' s'

y
s
(eq. 2)
where f is the focal length of the lens, M is the
magnification, s and s’ are the object and image
 respectively, and y and y’ are the object
distances,
and image heights. The trick in using eq.1 and eq. 2
is the correct assignment of signs. A focal length
• Cover the top half of the lens with an opaque
object. Your hand will do! Observe the effect on
the image.
• Reposition the lens and screen to obtain another
sharp image configuration. Repeat. Get enough
data (at least 15 data points) so that the screen is
moved over the entire length of the optical bench.
When you graph and analyze your data you can
decide if more data is needed. If you think you need
more then go back and get it.
• Measure and record the height of the object and
that of the image at one data point. Be sure to note
if the image is upright or inverted.
15-2
PHYSICS EXPERIMENTS — 132
• Graph the data with the image distance on the
vertical axis and object distance on the horizontal
axis. Determine the focal length of the lens from
the asymptotes of the graph using eq. 1.
• Graph the data with the reciprocal image
distance on the vertical axis and the reciprocal
object distance on the horizontal axis. Measure the
slope and intercepts of this graph. Determine
whether your graph verifies eq. 1 and find the focal
length of the lens.
• Use the measured image and object heights to
compute the magnification. Check eq. 2 using the
appropriate image and object distances.
Part B. Diverging Lens.
• Carefully
construct
a
compound
lens
combination with your converging and diverging
lens as shown in Figure 2. Check to be sure there is
a rubber o-ring between the two lenses. Tighten the
retaining screw just enough to hold the lenses in the
holder. Tightening too much may break the
diverging lens.
before
after
Figure 2. Two lens combination
• Mount the lens combination on the optical
bench and find one single sharp object-lens-image
configuration. Measure and record image and
object distances.
• Use eq. 1 to determine the effective focal length
feff. Use eq. 3 and the converging lens focal length
you determined in Part A to determine the focal
length of the unknown diverging lens.
Questions (Answer clearly and completely).
1. Is your converging lens data consistent with the
thin lens eq. 1?
2. What happens to the image if the top half of the
converging lens is covered?
3. What value do you determine for the converging
lens focal length from the asymptotes of the image
vs. object graph in Part A? What value do you
determine for the converging lens focal length from
the reciprocal image vs. reciprocal object graph in
Part A? Which value do you think is better?
4. Does the orientation of the lens combination in
Part B (which lens is in front) matter?
Refer to eq. 3 and try it!
5. What value do you determine for the diverging
lens focal length in Part B? How do you know from
the focal length that the lens is diverging?
6. Can you combine any converging lens in contact
with any diverging lens to make a system which
forms real images?