Physic 214 Laboratory
Images and Lenses
Pre-lab exercise: Consider two lenses, with focal lengths f 1 = 75 mm, and f2 = 150 mm placed
on an optical bench separated by 45 cm. The object is placed 20 cm in front of the first lens.
Where will the final image be located? Is it real or virtual? What is the image’s magnification
(include both magnitude and sign).
Equipment: Vernier caliper, two lens benches joined together, object box (light source), half
screen, 50 mm focal length spherical mirror, 75 mm, 150 mm, and – 150 mm focal length
lenses.
Theory: Thin lenses are lenses for which the lens thickness is small compared to the radii of
curvature of the lens, the object distance, and the image distance. For thin lenses the following
equation is valid
1 1 1
 
p i f
(1)
where f is the focal length of the lens, p is the distance of the object from the lens, and i is the
distance of the image from the lens. The lateral magnification of the image is
M 
i h
 ,
p h
(2)
where h' is the height of the image and h is the height of the object. The sign of the
magnification indicates whether the image is inverted (for negative M), or upright (for positive
M).
Spherical mirrors follow the same equation for object and image and magnification as
that for lenses. In addition the focal length is known to be ½ the radius of curvature.
In this lab we will investigate the properties of thin lenses and spherical mirror. In addition, we
will investigate images formed by combinations of two lenses.
Procedure and Calculations:
NOTE: When two lens bench sections are clamped together the metric scales on the
benches have a gap between them. You must measure the gap and correct the distance
measurements for that gap.
I.
Spherical (concave) Mirror
1. Set up the light source, half
screen and spherical mirror on the
optical bench, placing the concave
surface facing the light source with
the half screen in between the mirror
and light source. Be sure that the
mirror is more than 20 cm from the
source.
2. Record the distance between the
mirror and the real image and use
equation 1 to calculate the focal
length of the mirror.
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3. Using the vernier caliper measure the size of the image. Record appropriate object size
by reading the horizontal scale on the object box (light source). Compare with the
calculated magnification using the image and object distances (equation 2).
4. Calculate the radius of curvature of the mirror.
5. The radius of curvature of the mirror can be measured directly by locating the position
where the image and object distances are the same. Attempt to locate this distance from the
source to the lens by locating the image on the light source. (You may need to mask a
portion of the light source with an index card.) What is the magnification of the image for
such an arrangement?
II. Single Converging (positive focal length) Lens
1. Set up the object box, a converging lens, and the half screen on an optical bench (in
that order). Place the half screen at a distance from the source equal to at least 5 times
the focal length of the lens being measured.
2. Move the lens along the lens bench until you locate a sharp image on the screen.
Record the object distance, image distance, object height, image height and orientation
for this arrangement. Don’t forget to account for the scales on the two sections of
the light bench.
3. Move the lens (DO NOT MOVE THE HALF SCREEN) to another location where there is
a sharp image on the screen. Record the same data as above for this lens position. Is
there anything that you notice about the two pairs of image and object distances?
4. Repeat steps 1, 2, and 3 for the other converging lens.
5. Use equation (1) to calculate the focal length of each lens.
6. For each lens, use equation (2) to predict image height and orientation using your
measured values for p, q and h. Compare your observed and predicted values.
III. Two (converging) lens system
Recalculate the pre-lab problem using the actual focal lengths you calculated in part II for
each lens you will use. Set up the two lens system described in the pre-lab exercise as
follows:
1. Place the first lens 20 cm from the object box.
2. Measure the image and object distances to the first lens.
3. Place the second lens at the correct distance from the first.
4. Measure the final image distance from the second lens.
5. Also measure the final image height as well as the object height.
6. Compare these measured image and object distances and the magnification them with
your calculations?
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IV. Two (one converging and one diverging) lens system
1. A diverging lens’s focal length can
be measured by placing it in line
with a strong converging lens and
measuring the location of a real
object. Choose your shortest focal
length converging lens and place
it at least 25 cm from the light
source. Record your actual object
distance.
2. Locate the real image formed by this lens. Record the image distance.
3. Place the diverging lens next to the converging lens (and between the converging lens
and the screen). Record the distance between the two lenses.
4. Move the screen until you determine the location of the new real image. Record the new
image distance from the diverging lens.
5. Calculate the focal length of the diverging lens from by using the distance from the first
image (converging lens only) to the diverging lens as an object distance. Note: Be sure to
include the correct sign for the image distance for the diverging lens.
6. Measure the magnification of the system of lenses and predict the same using equation
2 as required.
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