Geometric Optics

Geometric Optics

Group Member Names:
In this lab, you will explore the images formed by lenses. The operating principle behind lenses is
refraction. Since light travels more slowly through glass than air, light rays bend (or “turn”) when they
enter or leave glass. Lenses are curved pieces
of material that either bend light rays together or bend
them apart.
Lenses are characterized by their effects on parallel rays:
A converging lens takes incoming parallel rays and
bends them toward each other. The rays will then
“converge”, meeting
at a point after the lens called the
focal point. The “stronger” the lens is, the more the
rays bend together, and the shorter the focal length
(i.e. the distance between the lens and the focal point)
.
A diverging lens takes incoming parallel rays an
d ben
d
s
them away from each other. The rays will then
“diverge”, spreading farther apart as they travel after
the lens.
After the lens, the rays appear to emanate
from a point before the lens, so a diverging lens can be
thought of as having a focal point
before the lens. The
“stronger” the lens is, the more the rays bend apart,
and the shorter the focal length.
The Lens Equation
:

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Since lenses bend rays closer together or farther apart, they will form images of objects. In other
words, if we view the
light rays after a lens, we’ll see an image of an object in front of the lens that
appears to be in a different place. The image can have a different size, location, and/or orientation
than the original object. As long as the light rays have only small
angular deviations from the
horizontal, we can use geometry to derive a relationship between the location of the object, its image,
and the focal length of the lens. This relationship is called the “
lens equation
”:
f
s
s
i
o
1
1
1
?
?
Where
s
o
= object distance
s
i
= image distance
f
= focal length of the lens
The sign conventions for
lenses
are:
Note that all distances are measured from the lens.
The image distance tells us the location of the image. To find how the appearance of the image is
changed, we define the magnification as the ratio of the image size
(height) to the object size (height):
o
i
h
h
m
?
Again using geometry for nearly parallel rays, we can derive a relationship between magnification and
the object and image distances:
o
i
o
i
s
s
h
h
m
?
?
?
This lab investigates these
relationships by projecting images from lenses.
Quantity
Symbol
Sign Convention
Object Distance
s
o
+ before lens
-
after lens
Image Distance
s
i
+ after lens
-
Before lens
Focal Length
f
+ after lens
-
Before lens
Activity A: Measuring the focal length of a lens
Your goal is to measure the focal length of a converging lens using the lens equation. You’ll also check
the magnification relationship.
The image for t
his experiment is a card with a lett
er F punched out as holes. The object is illuminated
from behind with a light bulb.
1)
Construct the pictured setup using a meterstick
and the lens and screen clips provided. The object
screen should be at the 10 cm mark, the lens at the 30 cm mark.
2) Measure the height of your object (the letter F) and record it in the data table.
3) Adjust the image screen position until the imag
e is as sharp as possible. You’ll probably need to
move
the image screen
back and forth a few times to find the location that gives the sharpest image.
4) Record the following in the data table:
?
Object distance (distance between the object and the lens)
?
Image distance (distance between the lens and the image screen)
?
Image height (height of the image on the screen)
?
Image orientation (upright or inverted)
5) Calculate the observed magnification (image height / object height)
6) Calculate
?
the focal len
gth of the lens using the lens equation
?
the theoretical magnification (
-
s
i
/s
o
)
?
the magnification percent error
7) Repeat steps 3
-
6 for the object distances
given in the table
plus at least 3 others of your choosing
Object Height h
o
= ____________
S
0
(cm)
S
i
(cm)
H
i
(cm)
Orientation
(inverted/upright)
Observed
Magnification
(h
i
/h
o
)
Theoretical
Magnification
(
-
s
i
/s
o
)
Magnification
% error
Calculated
focal length
(cm)
20
25
30
40
50
Average
f
= __________ cm
Accepted
f
= __________ cm
% error = _____________
Calculate the average focal length of the lens from all your trials. Obtain the accepted value from your
instructor and report a percent error for your measurements. Show
your work.
Activity B: Blocking the lens
In this activity, you will see what happens when you partially obstruct the lens. There are two
parts to each question, a prediction, a trial, and then an explanation.
1) Set up the original situation with
the object, converging lens, and image screen. As before,
adjust the image screen to get the sharpest image possible.
2) PREDICT what you think will happen if you cover the top half of the lens with a card. (don’t
do it yet) What do you think the ima
ge will look like?
Prediction:
3) TRY IT. What does the image actually look like?
How does blocking
the top half of
the lens
change the image?
Actual Result:
4) EXPLAIN IT: work together with your group to figure out why the image behaves this way.
Explanation:

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