Download Experiment 15

PHYSICS EXPERIMENTS — 132
7-1
Experiment 7
Simple Lenses
In this experiment you investigate image
formation by a 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 will verify thin lens theory and
determine the lens focal lengths.
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.
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
distances, respectively, and y and y’ are the object
and image heights. The trick in using eq.1 and eq. 2
is the correct assignment of signs. A focal length
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.
Focal length for a diverging lens is negative and
a simple diverging lens does not produce a real
image. A virtual image forms where the backwards
extensions of diverging rays cross and it cannot be
viewed on a screen. However, combining a
converging lens with a diverging lens may result in
a real image that can be viewed on a screen.
Procedure.
Part A. Converging Lens.
 Object at Infinity: In this part you will make a
single measurement of the image distance s¢ with
the object distance s @ ¥ . Hold the lens in one hand
and the screen in the other hand. Focus the image of
a distant bright object (such as a window across the
room) on the screen. Have your partner measure the
distance from the lens to the screen. This is the
image distance s¢ . Use this measurement to
calculate the focal length of the lens.
 In this part, you will determine the focal length
by measuring several pairs of object and image
distances and plotting 1/s versus 1/s’. Place the light
source and the screen on the optics bench 115 cm
apart with the light source’s crossed-arrow object
toward the screen. Place the lens between them as
shown in Figure 2.
1.15 m
Light source
Lens
Screen
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7-2
lens.
Figure 2. Experimental set-up for converging lens
1. Starting with the lens close to the screen, slide
the lens away from the screen to a position where a
clear image of the crossed-arrow object is formed
on the screen. Measure the image distance and the
object distance. Measure the object size and the
image size for this position of the lens.
2. Without moving the screen or the light source,
move the lens to a second position where the image
is in focus. Measure the image distance and the
object distance. Measure the object size and image
size for this position also. Note that you will not see
the entire crossed-arrow pattern. Instead, measure
the image and object sizes as the distance between
two index marks on the pattern.
3. Cover half of the lens with an opaque object
(you can use the lens-holder with white semicircular
plastic in the lens mount). Observe the effect on the
image.
4. Repeat steps 1 and 2 with light source-to-screen
distances of 110-85 cm by 5 cm increments. For
each light source-to-screen distance, find two lens
positions where clear images are formed. (You
don’t need to measure image and object sizes.)
 Place the diverging lens (with focal length -150
mm) on the bench at the 30 cm mark. Place the light
source at the 10 cm mark with the crossed-arrow
object toward the lens. Record the object distance s
(the distance between the light source and the lens).
Look through the lens toward the light source (see
Figure 3). Describe the image. Is it upright or
inverted? Does it appear to be larger or smaller than
the object?

Look through the lens
Light source
Lens
Figure 3. Observing a virtual image
 Without removing the light source and the
diverging lens, place the converging lens with focal
length +200 mm on the bench anywhere between
the 50 cm and 80 cm marks. Place the viewing
screen behind the converging lens (see Figure 4).
Slide the screen to a position where a clear image is
formed on it. The real image you see on the screen
is formed by the converging lens with the virtual
image (formed by the diverging lens) acting as the
object.
5. Plot 1/s versus 1/s’ and find the best-fit line
(linear fit). This will give a straight line with the xand y-intercepts equal to 1/f. Find the slope and x
and y intercepts of your graph. Is the slope
consistent with equation 1? Average the two values
of the focal length you obtained from the intercepts.
6. For the first two data points only (1.15 m
source-to-screen distance, at each position of the
lens), use the image and object distances to
calculate the magnification, M. Check your results
by
calculating
magnification
from
your
measurements of the image size and object size.
Part B. Diverging Lens.
A virtual image cannot be viewed on a screen. You
can see a virtual image by looking at it through a
Figure 4. Experimental set-up for the converging lens
 Measure the image distance s’ for the
converging lens (between the converging lens and
the screen). Using this measurement and the known
focal length of the converging lens, calculate the
object distance for the converging lens.
 Make a sketch of the location of each optical
component, similar to figure 4, and mark the
location of the object for the converging lens (this is
also the location of the virtual image formed by the
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diverging lens.) Now you know the object and the
image distance for the diverging lens, use them (be
careful with the signs of your object and image
distances) to find the focal length of the diverging
lens and compare with the given value.
Questions (Answer clearly and completely).
1. Is your converging lens data consistent with the
thin lens formula given by equation 1? What value
did you obtain for the slope?
2. (a) What value did you determine for the
converging lens focal length using an object at
infinity in Part A? What is the percentage difference
between the given focal length and this value?
(b) What value did you determine for the
converging lens focal length from the 1/s vs. 1/s’
graph in Part A? What is the percentage difference
between the given focal length and this value?
3. What happens to the image if half of the
converging lens is covered?
4. When you looked through the diverging lens
toward the light source (as in Figure 3) was the
image upright or inverted? Did it appear to be larger
or smaller than the object?
5. What value did you determine for the diverging
lens focal length in Part B? What is the percentage
difference between the given focal length and this
value?
6. Challenge question: For the converging lens case,
with a source-to-screen distance of L, show that no
image will form if L < 4f. Compute that minimum
distance for the converging lens in this lab.
rev. 10/13