Date
Period
Name
18-2
Convex and Concave Lenses
Objectives
Demonstrate the
formation of images
from concave and
convex lenses.
Define the characteristics
of the images formed
by concave and convex
lenses.
Analyze image size
versus distance for a
concave lens.
A convex, or converging, lens is thicker in the middle than at the edges. A
concave, or diverging, lens is thinner in the middle than at the edges. The
principal axis of the lens is an imaginary line perpendicular to the plane
that passes through the lens’s midpoint. It extends from both sides of the
lens. At some distance from the lens along the principal axis is the focal
point (F) of the lens. Light rays that strike a convex lens parallel to the
principal axis come together or converge at this point. The focal length
of the lens depends on both the shape and the index of refraction of the
lens material. As with mirrors, an important point is located at a distance
twice the focal length. If the lens is symmetrical, the points F and 2F are
the same distance on both sides of the lens, as shown in Figure A.
Interpret a graph to find
the focal length of a
concave lens.
Figure A
Focal length, object distance, and image distance are
measured from the lens along the principal axis.
Copyright © by Glencoe/McGraw-Hill
A concave lens causes all incident parallel light rays to diverge. Rays
approaching a concave lens parallel to the principal axis appear to intersect on the near side of the lens. Thus, the focal length of a concave lens
is negative. Figure B shows the relationship between the incoming and
refracted rays passing through a concave lens.
The distance from the center of
the lens to the object is do,
and the distance
from the center
of the lens to the
image is di. The
lens/mirror equation is
1
1
1
} 5 } 1 }.
f
di
do
Figure B
The focal length of a concave lens is negative. All
light rays that pass through a concave lens diverge.
Physics: Principles and Problems
Laboratory Manual 135
18-2
Name
Physics Lab
In this activity, you will measure the focal length, f, of a convex lens
and place an object at various distances from the lens to observe the location, size, and orientation of the images. You will find the focal length
of a concave lens by tracing diverging rays backward to a point of intersection. Recall that real images can be projected onto a screen; virtual
images cannot.
Materials
Procedure
A. Focal Length of a Convex Lens
double convex lens
concave lens
meterstick
meterstick support
To find the focal length of the convex lens, arrange your lens, meterstick, and screen as shown in Figure C. Point the lens at a distant
object and move the screen back and forth until you obtain a clear,
sharp image of the object on the screen. A darkened room makes the
image easier to see. Record in Table 1 your measurement of the focal
length. Compute the distance 2F and record this value in Table 1.
small cardboard screen
light source
holders for screen, light
source, and lens
metric ruler
sunlight
Figure C
B. Convex Lens
Figure D
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Laboratory Manual
2. Move the light source to 2F. Move the screen back
and forth until a clear, sharp image forms on the
screen. Record in Table 2 your measurements of
do, di, and hi and your observations of the image.
Physics: Principles and Problems
Copyright © by Glencoe/McGraw-Hill
1. Arrange the apparatus as shown in Figure D.
Place the light source somewhere beyond 2F on
one side of the lens and place the screen on the
opposite side of the lens. Move the screen back
and forth until a clear, sharp image forms on the
screen. Record in Table 1 the height of the light
source (object), ho. Record in Table 2 your measurements of do, di, and hi and your observations
of the image.
18-2
Name
Physics Lab
3. Move the light source to a location between F and 2F. Move the screen back and forth until a clear,
sharp image forms on the screen. Record in Table 2 your measurements of do, di, and hi and your
observations of the image.
4. Move the light source to a distance F from the lens. Try to locate an image on the screen. Record
your observations in Table 2.
5. Move the light source to a position between F and the lens. Try to locate an image on the screen. Look
through the lens at the light source and observe the image. Record your observations in Table 2.
C. Concave Lens
Place a concave lens in a lens holder and set it on the meterstick. Place a screen on one side of the
lens. Use one of the following procedures to determine the focal length.
Sunlight: Allow the parallel rays of the sun to strike the lens along the principal axis so that an image
forms on the screen. CAUTION: Do not look directly at the sun or you may severely damage your eyes.
The image should be a dark circle inside a larger, brighter circle. Place the screen close to the lens.
Quickly measure the distance from the lens to the screen and the diameter of the bright circle.
Record these data in Table 3. Move the screen to five other positions and repeat the measurements.
He-Ne laser: Shine a laser beam through the concave lens so that an image forms on the screen.
CAUTION: Do not look directly at the laser source or you may severely damage your eyes. Measure the distance from the screen to the lens and the diameter of the circle of light projected onto the screen.
Record these data in Table 3. Move the screen to five other positions and repeat the measurements.
Data and Observations
Table 1
Copyright © by Glencoe/McGraw-Hill
Focal length, f
2F
Height of light source, ho
Physics: Principles and Problems
Laboratory Manual 137
18-2
Name
Physics Lab
Table 2
Beyond 2F
Position of object
(cm)
At 2F (cm)
Between 2F
and F (cm)
At F (cm)
Between F
and lens (cm)
do
di
hi
Type of image: real,
none, or virtual
Direction of image:
inverted or erect
Table 3
Distance from lens (m)
Diameter of screen image (cm)
Copyright © by Glencoe/McGraw-Hill
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Physics: Principles and Problems
18-2
Name
Physics Lab
Analysis and Conclusions
1. Use the data from Table 2 to summarize the characteristics of images formed by convex lenses in
each situation.
a. The object is beyond 2F.
b. The object is at 2F.
c. The object is between 2F and F.
d. The object is at F.
e. The object is between F and the lens.
Copyright © by Glencoe/McGraw-Hill
2. For each of the real images you observed, calculate the focal length of the lens, using the lens/mirror
equation. Do your values agree with each other?
3. Average the values for f found in question 2 and calculate the relative error between this average
and the value for f from Table 1.
Physics: Principles and Problems
Laboratory Manual 139
18-2
Name
Physics Lab
4. Use your data in Table 3 to plot a graph on a sheet of graph paper of the image diameter versus the
distance from the lens. Place the image diameter on the vertical axis and the distance from the lens
on the horizontal axis. Allow room along the horizontal axis for negative distances. The rays expanding from the lens appear to originate from the focal point. Draw a smooth line that best connects
the data points and extend the line until it intersects the horizontal axis. The negative distance along
the horizontal axis at the intersection represents the value of the focal length. What is the focal
length you derived from your graph? If your lens package includes an accepted focal length, calculate the relative error for the focal length you determined. Use your graph paper for calculations.
Extension and Application
1. Use two identical, clear watch glasses and a small fish aquarium to investigate an air lens. Carefully
glue the edges of the watch glasses together with epoxy cement or a silicone sealant so that the unit is
watertight. Attach the air lens to the bottom of an empty fish aquarium with a lump of clay and put an
object nearby, as shown in Figure E. Observe the object through the lens and record your observations.
Predict what will happen when the aquarium is filled with water and light passes from a more dense
medium to a less dense one as it passes through the air lens. Fill the aquarium with water and repeat
your observations. Compare the two sets of observations. Explain your results. What would you expect
if you used a concave air lens? Design and construct a concave air lens to test your hypothesis.
Figure E
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Laboratory Manual
Physics: Principles and Problems
Copyright © by Glencoe/McGraw-Hill
2. The movement of reflected laser light relative to an observer’s moving head can be used to determine nearsightedness or farsightedness. Observers should remove their glasses or contact lenses. In
a darkened room, use a concave lens to expand the beam diameter of a laser to project a large spot
on a screen. Observers should move their heads from side to side while looking at the spot. Each
student should record the direction in which the reflected speckles of laser light appear to move
and the direction in which his or her head is moving. Then observers should replace their glasses
or contact lenses and repeat their observations.