Thin Lenses
PURPOSE:
To investigate methods for finding the focal lengths of thin lenses and verify the thin lens equation.
APPARATUS:
Optical bench with carriage and lens holders
Clear filament incandescent lamp and socket
Bench mounted incandescent lamp
Ground glass screen
Object lamp for optical bench
Converging lenses (f = 10 cm and 20 cm)
Small plane mirror
Lab stand with crossbar and clamp
METHOD:
In this experiment you will find the focal lengths of two converging lenses by three different methods and
of one diverging lens by two methods. Many of the methods involve using the thin lens equation:
s
1
s
1
f
Equation 1
where s is the object distance (object to lens), s' is the image distance (image to lens), and f is the focal length. For
real objects and images the distances are positive. For virtual objects and images the distances are negative. Focal
lengths are positive for converging lenses (thicker in the middle than at the edges) and negative for diverging lenses
(thinner in the middle than at the edges).
METHOD I: CONVERGING LENS WITH DISTANT OBJECT
When the object is very far away, s = ∞, and equation 1 gives s'= f. Thus the focal length is found by
measuring the image distance for a distant object.
PROCEDURE I:
1.
Place two carriages with lens holders on the optical bench. Place one of the converging lenses in one
holder and the ground glass screen in the other.
2.
Move the carriage with the lens to the center of the bench and turn the bench so that the light from some
distant source (at least 5 meters away) lines up with the lens and the screen on the other side of the lens.
Clamp the lens carriage down.
3.
Move the carriage with the ground glass screen along the bench until the image of the distant object is
sharply focused on it (the screen holder may need to be raised or lowered in its carriage). Clamp down the
screen carriage.
4.
Using the scale on the side of the bench and the index marks on the carriages, find the image distance.
Record this distance as f.
5.
Repeat steps 1 through 4 with the other converging lens.
METHOD II: CONVERGING LENS WITH OBJECT ON THE OPTICAL BENCH
In this method a real object at a finite distance is used and the focal length is calculated from the measured
image distance and equation 1.
PROCEDURE II:
1.
Place two carriages on the bench 100 cm apart and clamp them down. In one put a lens holder with a ground
glass screen and in the other put the bench incandescent lamp.
2.
In between these two place another carriage with lens holder and one of the converging lenses.
3.
Adjust the lamp so that the filament is perpendicular to the axis of the optical bench. Adjust the height of all
elements so that the filament is just at the same height as the center of the lens and the screen.
4.
Turn on the lamp and move the lens carriage along the bench until a clear image of the lamp is formed on
the screen. Clamp down the carriage.
5.
Using the scale on the bench and the index marks on the carriages find the object and image distance and
record as s and s'.
6.
Move the lens to find the other object and image distances that produce a clear image. Because the image
will be very large, use a large sheet of paper at the position of the screen to help locate the image. Record
these values as S and S'.
7.
Repeat steps II,4 through II,6 for the other converging lens.
METHOD III: CONVERGING LENS BY AUTOCOLLIMATION AND PARALLAX
This method uses a process called autocollimation. If a small object is precisely at the focal point of a
converging lens, all light rays from the object which pass through the lens will form a parallel beam along the axis
on the other side of the lens. A plane mirror placed perpendicular to the collimated beam will reflect the rays so
thatthey return to the lens in a parallel beam and focus back down to the focal point. In other words a real image
will be formed at the position of the object. For an object you will use a pencil point or the tip of a ball point pen.
See figure 1.
You will determine the position of the image by using the effect called parallax. Parallax is the apparent motion of
two objects with respect to each other, due to a real motion of the observer: objects closer to the observer appear to
move past objects more distant. In this part of the experiment, when you view the object and image together, you
can tell they are at the same position if they exhibit no parallax as you move your head from side to side. Figure 1
illustrates the final situation you will try to attain.
PROCEDURE III:
1.
Position yourself and the optical bench so that you can sit and comfortably look along the axis.
2.
About 40 cm from your end of the bench place two carriages as close together as possible. The nearer one
should have a lens holder with the longest focal length converging lens and the other should have a lens
holder with the plane mirror facing the lens. Clamp both carriages down.
3.
Place a third carriage on the bench between the lens and your end of the bench. In this carriage insert a
long sharp pencil or ball point pen and adjust all elements in height so that the point of the object is just at
the level of the middle of the lens and mirror.
4.
Move the object carriage along the bench while looking along the bench, through the lens, and into the mirror,
until you can see an inverted image of the object. Adjust the angle of the mirror in order to make the image
appear just above the object.
5.
Move your head from side to side and observe any parallax (relative motion) between the object and the
image.
6.
If the object appears to move more than the image, it is closer to you; move the object toward the lens slightly
and repeat step III 5.
7.
If the object appears to move less than the image, it is farther from you; move the object slightly away from
the lens and repeat step III 5.
8.
When the object and image appear to move together (no parallax), they are at the same position. Clamp the
object carriage down. Using the scale on the side of the bench and the index marks on the object carriage and
lens carriage, determine their separation. Record this separation as f.
Thin Lenses Lab Sheet 1
DATA TABLE:
Method 1
Lense 1
Lense 2
Method 2
Lense 1
Lense 2
f
s
s'
S
S'
Method 3
f
CALCULATIONS: SHOW ALL WORK
1. From the data of steps 5 and 6 in Method II and equation 1, calculate two values of f for each of your
converging lenses. Average the two values for each lens and enter them into your results section.
2. Calculate the percent difference between Methods I and II. Enter these percents into your results
table.
3. Calculate the percent difference between Methods I and III. Enter this percent into your results table.
RESULTS TABLE:
Method II
f
% Difference I &II Method
Lense 1
I
Lense 2
III
CONCULSION: TURN IN LAB SHEET 1
% Difference