Characterizing Lenses
Lenses are not all the same. How do we measure and describe their differences?
> A laser beam is directed towards a wedge made of some transparent material. Where
does it come out the other side?
> Show what happens to three parallel laser beams when they encounter the six-sided
object made of the same material.
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Characterizing Lenses
Lenses are not all the same. How do we measure and describe their differences?
Materials
 1 large round convex (positive) lenses (“A”)
 1 small round convex (positive) lens (“B”)
 2 different positive Fresnel (card) lenses (called
“C” and “D”)
 1 negative Fresnel lens (“E”)
 Various other lenses
 White card
We will do this first part together, in the lobby on the first floor
 Use a lens to make images of a distant scene out the window on a white card.
The white card is your screen.
 Try different lenses to see if their images differ.
What happens to the image when you cover part of the lens with your hand?
1. You have 4 lenses to compare, labeled A, B, C, and D. For each lens, focus an
image of a distant scene on the card and measure the distance from the lens to the
card. This distance is the focal length of the lens. Record the focal length of each
lens in the table. Fill in rows 2 and 3 by following the instructions in each row (row
4 is discussed later). Some of the boxes will be blank.
Lens
A
B
C
D
1.
focal length (cm)
2. Mark which lens has largest, and
which the smallest focal length
3. Compare the sizes of the images.
Indicate which lens makes the biggest
image, and which makes the smallest
image.
4. . Which lens is the best magnifier and
which is the weakest?
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2. Compare focal lengths and image sizes (use lines 1, 2 and 3 in the table). What effect
does the focal length of a lens have on the size of the image it makes?
3. What effect does the size of a lens have on the image it makes?
4. Use the lens like a magnifying glass to read the print on this page. Which lens makes
the best magnifier? Which lens do you hold closest to the paper? Referring to lines 1,
2 and 4 in the table, how is the magnification of a lens related to the focal length?
More about refraction
How prisms are related to lenses
1. In diagram A, below, show what will happen to a laser beam directed towards a
wedge made of some material. In diagram B, show what happens to three parallel laser
beams.
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2. In diagram B, the light beams cross somewhere (“the focal point”) after going
through the six-sided object. Suppose instead there were a light source at the focal
point, emitting light towards the six-sided object. What would happen to these light beams?
3. If we want every parallel beam to go to the same focal point, we need an object with a
curved surface (a lens). On this diagram, continue the lines to show how the light beams
come together at the focal point.
4. Another way to accomplish this is to use many wedge-shaped pieces (this is called a
Fresnel lens (the word is pronounced “fre-NELL”). Draw lines showing how all the
light beams come together at the focal point.
Check: discuss these questions with an instructor
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5. Lighthouses are put on reefs and islands to warn ships. If an ordinary light source
(that sends light in all directions) is used, most of the light is wasted. Draw lines
showing the light beams.
6. The solution to the light house problem is to use a Fresnel lens to direct most of the
light towards the ships. Assume the light source is placed exactly at the focal point of
the lens, and draw some lines showing how the light is redirected
7. A bottle of water makes a shadow, even though the plastic and the water are
transparent. Explain how this works. A sketch might be useful.
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8. The table lamp now has a small unfrosted light bulb in it. Place the viewing screen
(standing upright) at some distance from the light bulb, and make an image on the screen
using lens A.
9. How does this image change if you move the lens a few centimeters closer to the
screen or farther from it (not moving the screen)?
10. Is there only one place that gives a focused image, or several places?
11. Replace the lens with a mask with a very small hole in it. This also gives an image
on the screen. Compare this image to that made by the lens when they are the same
distances from bulb and screen: how are they similar, and how are they different.
12. Compare the images made by lens A to the images made by lens B.
13. Change the position of the viewing screen so that it is twice as far (or half as far) from
the light bulb. How does this change where you have to put the lens to get an image, and
how does it change what the image looks like?
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Each group should hand in one copy of this page
Group:
Names of group members present:
14. A fish is swimming in a calm clear pond, and a bird is flying over the pond. Draw
some lines that show how the fish can see the bird, and how the bird can see the fish.
From the point of view of the fish, in what direction does the bird seem to be?
the path that light takes.
From the point of view of the bird, where does the fish seem to be?
that light takes.
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Draw in
Draw in the path
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Check:
A large focal length lens has to be far from the viewing screen to give a focused image.
The image is large. A short focal length lens gives a small image.
The size of the lens affects the brightness of the image; but large focal length lenses have
to be large lenses, so one gets the impression that large lenses make large images (and
they do, but there are small lenses with a long focal length, and these give large dim
images).
Short focal length lenses let you look at an object close up (holding both object and lens
close to your eye), and make good magnifiers. You can also look at the object with the
lens close to it (and both farther away). The short focal length lense continues to be the
better magnifier.
Positive lenses will make images on a card; they are upside down. Negative lenses will
not make an image on a card.
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The prism
The light beams can both reflect and refract at every surface they encounter.
“Reflect” means the light beam stays on the same side of the surface (if it is in, it stays
in), and the incoming and outgoing beams are related by the “equal angles” rule.
“Refract” means the light beam goes through the surface, and the incoming and outgoing
beams are related by a more complicated rule: as the light goes from air to being inside
the material, it becomes more nearly perpendicular to the surface.
Line a is the result of the reflection of the incoming beam at surface A. It is rather
weak, until we turn the prism a lot clockwise (the reflection is large when the incoming
beam is almost parallel to the first surface it encounters).
Line b is the result of refraction of the incoming beam at surface A. It is closer to the
perpendicular (the dashed line) than the original beam, because light has entered the new
medium.
Line d is the result of the reflection of beam b at surface B.
Line c is the result of the refraction of beam b. It is farther from perpendicular to surface
B, because the light is coming out of the medium. If we turn the prism just a little bit
clockwise, the outgoing beam c will cease to exist because beam b arrives too far from
perpendicular. Instead, all of beam b will be reflected to make beam d, which means that
beam e gets a lot brighter. When beam c is present, it will have a bit of color effect,
because blue light bends slightly more than red.
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13. A laser beam is directed towards a prism, as shown. Three visible light beams
result:
A) light that is reflected from the front surface,
B) light that enters the prism, travels to a different surface of the prism, and leaves it;
C) light that enters the prism, travels to a different surface of the prism where it is
reflected, travels to yet another surface (perhaps the first one, again), and leaves there.
Please draw in the path taken by these three beams (labeling them A, B, C)..
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