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Image Formation by Lenses
Purpose:
To verify experimentally the relationship between the object position, lens position,
and image position; to verify predictions of magnification by lenses; to determine the focal
length of an unknown lens
Apparatus:
Long and short magnetic optical benches; light source with diffuser; lenses; disposable
camera; screen
Introduction
If an object, a lens of focal length f, and a screen are positioned as shown in the
diagram, the relationship between the object-lens distance p, the image-lens distance q, and
the focal length is
(1/p) + (1/q) = 1/f
q
p
object
lens
(focal length f)
image
By convention, converging lenses have positive focal lengths and diverging lenses have
negative focal lengths. There is also a convention for interpreting the algebraic sign of
q:
q > 0
=> a real image (an image that will appear on a screen)
q < 0
=> a virtual image (one that can’t appear on a screen)
The linear magnification of an image is defined as the ratio of the image height to the
object height. This ratio can be shown to be the same as the ratio of the image distance to
the object distance. By convention, a minus sign is added to the definition to tell whether
the object is upright or inverted:
M = -q/p
M > 0
=> the image is upright (oriented like the object)
M < 0
=> the image is inverted (upside down relative to the object)
If the magnitude of M is greater than 1, the image is said to be enlarged.
Investigation 1
Set the light source on the short optical bench and place it behind the 0 end of the
long optical bench. Put the diffuser on the front of the light source. Position a magnetic
holder with its index mark at 0 on the long optical bench and put the crossed arrow object
on the side of the holder facing the light source.
Put a lens with f = + 127 mm on a lens holder and position that holder at 20.0 cm on
the bench.
 Stephen Luzader
Prediction
Calculate the expected image distance (the distance from the lens to the image), and
describe the nature of the image (real or virtual, upright or inverted, enlarged or not
enlarged). Do your calculations in the space below.
Predicted image distance = __________
Predicted nature of the image:
Now put the screen on a third magnetic holder and move it along the optical bench until
you see a clearly focused image. Record the position of the holder:
Measured position of image = _________
Describe the nature of the image:
From the positions of the object, lens, and image, figure out the object and image distances
from the lens, which are p and q respectively:
Calculations
Measured p = __________
Measured q = __________
Lenses 2
 Stephen Luzader
Were your predictions correct?
Explain briefly.
Investigation 2
We want to make an observation about how the light rays from the object actually pass
through the lens to form an image. For example, if we cover part of the lens, what will
happen to the image?
Prediction
Predict what will happen if the lens is partially covered by an index card that is held
right against the lens.
Describe what happens when the lens is partially covered by an index card.
the card is against the lens and not some distance away from the lens.)
(Be sure that
What can you conclude from this about how light rays from the object travel through the
lens? For instance, do rays from the top of the object only go through the top of the lens,
or does something else happen? Explain briefly.
Investigation 3
Leave the object at 0, and place the screen at 70.0 cm.
There are two positions
between the object and the screen where the lens can be placed to produce a real image on
the screen.
Your task is to predict where those two locations are and then test the
prediction experimentally.
(Hint:
If the object-screen distance is called D and the
object-lens distance is p, then the lens-image distance is q = D - p. Substituting this
into the lens equation gives a quadratic equation in one unknown, q.)
Prediction
Find the two values of q and use those to get predicted values of the lens position on
the optical bench. Also predict the nature of the image. Begin your analysis with a sketch
here and continue the calcuations on the next page.
Sketch
Lenses 3
 Stephen Luzader
Calculations:
First position of lens
Nature of that image
Second position of lens
Nature of that image
Lenses 4
 Stephen Luzader
Experimental Test
Now slide the lens holder along the bench to find experimentally the two positions
where the image is in focus. Record one position and the nature of that image here:
First position of lens
Nature of that image
Second position of lens
Nature of that image
Explain briefly how well your experimental test agreed with your predictions.
Investigation 4
You’ll be given a disposable 35 mm camera. The body of the camera consists of parts
that snap together, so you can carefully pull off the front plate and remove the small
plastic lens. Your task is to devise a method of determining the focal length of that lens.
Step 1 Describe the method by which you’ll determine the focal length.
position the lens and describe the calculations necessary.
Step 2
Tell where you’ll
Record your experimental object, lens, and image positions:
Object position = __________
Lenses 5
Lens position =
__________
Image position =
__________
 Stephen Luzader
Step 3
From these data, calculate the focal length of the lens.
Focal length of lens = __________
Lenses 6
 Stephen Luzader