SIMG 215 - Laboratory
Lens Focal Length
Objective: To measure the focal points of lenses, and to test the geometric theory of lens
focusing.
Equipment: This experiment requires the "Optics Discovery Kit" by OSA. Your
instructor will provide you with a masked light source, as shown below, and with graph
paper. Measure the height of the triangle on the light source, and note that the triangle is
pointed up. Your instructor will provide you with additional equipment to set up the
optical system shown in Figure 1.
Figure 1: Measuring the point of focus and the focal point.
paper
screen
lens
L'
L
h'
h
Triangular hole
Aluminum Foil Mask
Light Source
Lens
Holder
(I) Forming images with the lens:
Start with the larger lens, "A", and set up the experiment illustrated in Figure 2. Place the light
source at a distance L = 100 cm from the lens. Adjust the location of the paper screen to bring the image of
the light source into focus. Measure the two distances L and L ', and measure the size of the light source, h,
and the size of the image formed by the lens, h'. Record your data in Table I. Repeat the measurements for
the smaller lens, "B".
Table I: Data on Image Projection
Suggested values for L, in cm, for lenses A and B.
For Lens "A"
For Lens "B"
(II) Testing the Theory of Magnification:
The experimental system in Figure 1 uses the lens as an image projector, much
like a slide projector used to show 35 mm slides. The magnification of the image is the
ratio, h'/h. Use your measured values of h' and h in Table I and calculate magnification
values for both images "A" and "B". Record these values as M in Table I.
M
h'
h
(2)
Geometric theory tells us that magnification, M, is related to the distances, L and
L', by equation (3).
M
L'
L
(3)
Calculate the ratios L'/L, and record these in Table I. In order to show whether or not the
theory works for these lenses, plot the measured value of M versus L'/L.
(III). Method #1 for Estimating the Focal Point of a Lens:
The focal length, f, is a very important property of a lens. Note that the point of
focus, L', is not the same thing as the focal point. The focal point is defined as the point
of focus FOR THE OBJECT AT INFINITY (L = ). The focal length, f, is the value of
L' when L is at infinity.
f = L' at L= 
(4)
Since we can't really move L to infinity, we use a technique of extrapolation. Plot your
data as L' versus L. From your graph, estimate the trend in behavior, and estimate the value of L'
at L= . This extrapolated value of f is your estimate of the focal length. Plot a separate graph
for lens "A" and lens "B", and estimate the focal length for each lens.
(IV) Method #2 for Estimating the Focal Point:
Theory says that an object placed at twice the focal length, L = 2f, will produce a
focused image of magnification M = 1 at L' equal to L.
f = L/2 at M = 1 and L = L'
(5)
The dotted line on your graphs of L' vs L show all places where L' = L. Use your data to
estimate the point at which the trend in your data crosses this dotted line, and write down
this value of L. Divide this value by 2 and define it as the focal length measured by
method #2, f = L/2. Use this method to estimate the focal length of both Lens "A" and
Lens "B".
(V) Estimation of Experimental Uncertainty:
Experimental measurements always carry some degree of uncertainty, often called
"experimental error". Perfect precision is not possible. Therefore, experimental results
should always be reported with some estimate of the degree of uncertainty of the
measured result. There are many advanced techniques for estimating experimental
uncertainty, involving statistical evaluations of data. However, it is always essential for
the experimentalist to compare such statistical estimates of uncertainty with his or her
qualitative judgment of uncertainty. It is never correct to justify results by saying "that's
what the computer said".
Examine your graphs to estimate the degree of uncertainty in your estimate of the
focal lengths, f, made by the two methods. To help you make this judgement, an example
is shown in Figure 3. If you need help estimating experimental uncertainty, ask your
instructor for help.
Figure 3: Example of an estimate of experimental uncertainty.
300
Equal Point = 112 gives f = 56 cm
200
Extrapolation gives f = 48 cm
L
100
50
Uncertainty range = 50, or ± 25
50
100
200
300
400
L
(VI) Your Lab Report
Conclusions From Your Data
A. According to your data in Graph I, does the geometric law of magnification
apply to lenses A and B? (yes, no, or experimental error is too great)
B. From Graphs II and III, how does the size of the image change as the object moves
from infinity to zero?
C. Do methods #1 and #2 provide the same estimate of focal length? Your answer
should include something about the magnitude of uncertainty of your data.
Brain Teasers based on your experimental results
The following are examples of practical applications of the geometric theory of lens focal
point and magnification.
A. In an overhead projector, where is the overhead slide located relative to the focal
point of the projector lens? (Answer something like: "At the lens", or "At the focal point", or
"Between the lens and twice the focal point", or "Between zero and twice the focal point", etc.)
B. In a camera, where is the film located relative to the focal point of the camera lens?
(Answer something like: "At the lens", or "At the focal point", or "Between the lens and twice the
focal point", or "Between zero and twice the focal point", etc.)
[Hint: What magnifications are useful for overhead projectors and cameras?]
Graphing your Results
Graphs 1A and 1B: M Versus L/L'. A test of magnification theory.
Lens A
Lens B
M
4.0
4.0
3.0
3.0
M
2.0
2.0
1.0
1.0
0
0
0
1.0
2.0
3.0
0
4.0
1.0
2.0
3.0
L/L'
L/L'
[Note: The phrase "L'/L versus M" means that M is the abscissa (x axis) and L'/L is the
ordinate (y axis).]
Graph 2: L' versus L for Lens A.
400
300
L'
200
100
0
0
100
200
L
300
400
Estimate of f by Method #1:__________, uncertainty range:_________
Estimate of f by Method #2:__________, uncertainty range:_________
4.0
Graph 3: L' versus L for Lens B.
16
14
12
10
L'
8
6
4
2
0
0
10
20
30
40
L
Estimate of f by Method #1:__________, uncertainty range:_________
Estimate of f by Method #2:__________, uncertainty range:_________