Name:______________________________________________________
Lab Section: _______
Lab Partners: ___________________________________________________ Grade:____________
Physics 202
Experiment #6
Lenses
Pre-Lab
Pre-lab Questions (turn in at start of lab)
1. Draw an approximate ray diagram for the second part of part A from the converging lens portion of the lab.
Attach paper if necessary.
2. Draw an approximate ray diagram for part B from the diverging lens portion of the lab. Attach paper if necessary.
Name:______________________________________________________
Lab Section: _______
Lab Partners: ___________________________________________________ Grade:____________
Physics 202
Experiment #6
Lenses
Introduction
The locations of object and image in reference to a lens are given by the basic lens formula (for a thin lens)
1 1 1
 
p i f
(1)
where p = distance from object to lens
i = distance from image to lens
f = focal length of the lens
By convention, p is positive for a real object and i is positive if the image is located on the opposite side of the
lens from the object. For positive values of i, the image is real and may be projected onto a screen. For
negative values of i, the image is virtual, i.e., the rays of light coming through the lens diverge and appear to be
coming from an image located on the same side of the lens as the object. Virtual images cannot be projected
onto a screen.
There are two general types of lenses: converging and diverging. A converging lens is thicker in the middle than
at the edges and parallel rays of light passing through converge on the other side. A diverging lens is thinner in
the middle than at the edges and parallel rays of light passing through diverge on the other side.
The principal focus of a lens is the point (in the case of a converging lens) on the axis of the lens through which
all rays of light parallel to the principal axis pass, or (in the case of a diverging lens) appear to pass, when
refracted by the lens. The distance from the center of the lens to the principal focus is called the focal length of
the lens. A converging lens has a positive focal length and is therefore often called a positive lens. A diverging
lens has a negative focal length and is often called a negative lens. Careful attention to the signs of p, i and f is
necessary for the correct use of Equation 1.
Two points, such that an object at one produces an image at the other, are called conjugate foci.
The image produced by the lens may have a size different from that of the object. If h is the height of the object
and h’ is the height of the image, the magnification is defined as
h'
m
(2)
h
Which can also be written with reference to the object and image distances as
i
(3)
m
p
Note that the sign of the magnification refers to the image orientation. Positive is upright and negative is
inverted.
Converging Lens Procedure:
A. Focal length by parallel rays
Rays of light from distant objects are essentially parallel. For the purposes of this experiment, a building or
other object 50 meters or more away may be considered a distant object. Use the short optics bench that is
located in the discussion room or on the counter in lab. Take the converging lens and the telescope with you.
Put the converging lens in the optics bench and focus the image of an object located outside upon the screen.
Since the incident rays are essentially parallel, the image formed will lie in the principal focal plane of the lens.
Measure the distance from the center of the lens to the screen using the metric scale on the edge of the optics
bench after the best focus has been obtained. Record your first determination of the focal length.
Focus the telescope on some distant object outside. The telescope is now adjusted to focus parallel rays entering
it. Return to your optics bench and then plug in the light source and mount it so the object (crossed arrows with
two circles) is at the 10 cm mark. Mount the converging lens and the telescope. Look through the telescope and
move the lens toward and away from the object until the object appears clearly in focus in the telescope. If you
have problems with this step, you may need to adjust the telescope to find a clear image. Measure the distance
from the center of the lens to the object. Record your second determination of the focal length.
1) Why is this equal to the focal length? Refer to your sketch from question 1 of the pre-lab.
B. Focal length by conjugate foci
Remove the wire and the mirror and dim the desk lamp. Plug in the light source and mount it so the object is at
10 cm. The object is O in Figure 1. Mount the converging lens and the screen. Move the lens until the image is
well focused on the screen. The object and image are now at conjugate foci of the lens. You will measure the
distances from the object to the center of the lens (p) and from the center of the lens to the image (i). Use
Equation 1 to calculate your third determination of the focal length.
Without moving either the object or the screen, move the lens until another sharp image is projected onto the
screen. Once again measure the object distance (p) and the image distance (i). Use Equation 1 to calculate
your fourth determination of the focal length.
i
i'
Figure 1: Conjugate foci.
Denoting by b the distance between the object and the image and by a the distance between the two positions of
the lens, it may be shown that the focal length is given by
b2  a 2
f 
(4)
4b
Use Equation 4 to find the focal length. Note that b = p + i and a = p - p. This will be your fifth determination
of the focal length. Be sure that you have recorded all of your focal lengths and associated calculations in your
spreadsheet.
2) For each of the two conjugate foci find the magnification using Equation 2 and Equation 3.
3) Would you expect to get a more accurate value for m using Equation 2 in the situation where the lens is
closest to the object or in the situation where the lens is furthest from the object? Why?
Diverging Lens Procedure:
A. Focal length by virtual object
Without moving the object or the screen from the previous part, position the converging lens where you got the
smaller image. Now place the diverging lens between the converging lens and the screen. Its diverging action
will cause the image to lie farther from the converging lens than it did originally (see Figure 2).
i1
i2
Figure 2: Measurement of the focal length of a diverging lens.
Measure the distance from the screen to the center of the diverging lens (p2). Move the screen out until the
image is again in focus. Measure the distance between the center of the diverging lens and the screen (i2). In
this setup, the image I1 of the first lens serves as the object O2 of the second lens. This is a virtual object so p2 is
negative. The image I2 is real so i2 is positive. Use p2 and i2 in Equation 1 to calculate your first determination
of the focal length for the diverging lens.
B. Focal length by parallax
Turn off the light source, remove the converging lens and slide the screen to the end of the optics bench. Move
the diverging lens to the middle of the optics bench. Use the desk lamp for illumination. Mount the half-screen
opposite to the screen. The vertical edge of this half screen will serve as the object.
Looking through the lens at the object, determine the general location of the image. Mount the vertical wire at
the approximate location of the image as shown in Figure 3. Adjust the position of the wire as viewed above the
lens until its position coincides with the image of the object viewed through the lens. That is, slide the wire
mount until there is no relative movement between the wire viewed above the lens and the edge of the white
object viewed through the lens when you move your head from side to side.
Figure 3: Looking through the diverging lens.
Measure the distance from the center of the lens to the position of the object (p). Measure the distance from the
center of the lens to the vertical wire, which is now marking the image location (i). Use Equation 1 to calculate
your second determination of the focal length, putting in a positive value for p and a negative value for i.
4) Calculate the magnification m of the diverging lens using Equation 3 and your values of p and i from the
last part.
5) Describe the image in words: real or virtual, upright or inverted, enlarged or reduced.
6) Draw and label the ray diagram corresponding to Figure 3.
Post-lab Questions:
1) Do the focal length measurements for each of your lenses agree? Compare the different focal length
measurements with associated uncertainties. The uncertainties will be found by propagating the
uncertainty for each measurement.
2) What was the objective of this lab? Do you feel the objective was appropriately achieved? Why or why
not?
3) Name the two most significant sources of scientific error in this experiment (Be specific – do NOT say,
for example, “human error” or “equipment limitations”). Are these errors likely to be random or
systematic? Explain.
4) Describe some ways that the error in this lab could be reduced, including the possible purchase of
additional equipment. (Continue on the next page if necessary.)