Imaging - The Institute of Optics

Imaging
October 23, 2008
Authors:
Miguel Alonso, The Institute of Optics
Joe Malach, Corning Tropel
Andy Murnan, Genawave
Paul Murphy, QED Technologies
Revised By:
Jonathan Petruccelli, The Institute of Optics
Christopher Todd, The Institute of Optics
Write-up
Write-up ............................................................................................................................................
Overview .................................................................................................................................... 1
Background ................................................................................................................................ 4
Imaging Demonstrations...................................................................................................................
Pinhole camera ........................................................................................................................... 8
Flashlight illumination as a sum of images .............................................................................. 13
Lens camera.............................................................................................................................. 15
Forming an image with a concave mirror ................................................................................ 21
Forming an image with a soda bottle…………………………………………………………23
Single lens imaging Demonstration ......................................................................................... 27
Optical system demonstration……………………………………………………………………
Anatomy of a camera ............................................................................................................... 36
Overview
The basic idea
An optical image is a replication of an object using light, where the replication retains the
proportions of the original object. Imaging is the process of forming an image.
Dictionary definition
Im age \ ‘im-ij\ n : An optically formed duplicate, counterpart, or other representative
reproduction of an object, especially an optical reproduction formed by a lens or mirror.
Source: The American Heritage® Dictionary of the English Language, Fourth Edition Copyright
© 2000 by Houghton Mifflin Company.
1
To form an image, light emitted by or scattered from an object must be selectively allowed to
pass through a pinhole or collected and focused by a lens(es) or mirror(s). An obstacle with a
pinhole forms an image by blocking all light rays except for one (or a very thin bundle of them)
from each point of an object. Therefore, each point on a screen placed behind the pinhole
receives only one ray, coming from a corresponding point of the object, as shown in Figure 1.
Most light rays are blocked,
but a pinhole allows one
light ray to pass from each
point on the light bulb
Light bulb emits light
in all directions
An image of the light bulb is
formed on a screen
Figure 1: Pinhole forms image
A lens, on the other hand, forms an image by collecting a bundle of light rays from every point
on the object and focusing them to corresponding points on the screen. This is shown in Figure
2, where the gray area represents a bundle of rays collected and focused by the lens from one
point on the light bulb to the corresponding point on the screen.
Light bulb emits light
in all directions
Lens collects rays from each point of
the light bulb and images each point
onto a screen.
An image of the light bulb is
formed on a screen
Figure 2: Lens forms image
Definitions
Ray: Line along which the energy carried by light travels.
Focusing: The action of making a bundle of rays from a point on the object converge to a
corresponding point in the image.
2
Lens: a piece of glass, plastic, or other transparent material with smooth sides (at least one of
which is curved) that is used to change the direction of rays. Lenses that are thicker at the center
than at the edges have the capacity to focus light rays, and therefore to form real images. These
are called converging or positive lenses. Lenses that are thicker at the edges cannot form real
images on their own, but can be used in combination with converging lenses to make cameras of
better quality. They are called diverging or negative lenses. Lenses work by refracting light at
each of their surfaces. See Figure 3. Refraction follows Snell’s law.
θ2
θ3
θ1
n1
R1
n2
n3
θ4
R2
Figure 3: Lens showing a single ray refracting at both surfaces. The ray, coming from a medium with index
of refraction of n1, enters a lens whose material has index n2. The ray hits the lens’s first surface at an angle of
incidence of θ1 with respect to the surface’s normal. This surface, with radius R1, refracts the ray at an angle
θ 2 . The ray then travels to the second surface, hitting it at an angle θ 3 . Finally, the ray leaves the lens at an
angle θ 4 from the surface normal and enters a medium with index of n3. See refraction demonstration for
more information.
Real image: an image that can be projected onto a screen and is accessible. See Figure 4 Top.
Virtual image: an inaccessible image that appears to come from a particular point behind a lens
or mirror, but in fact comes from an object at another location. See Figure 4 Bottom.
Object
Real
Image
Object
Virtual Image
Figure 4: Top: Lens forms a real image of the object. Bottom: Lens forms a virtual image of the object.
3
Background
History
~500 BC The earliest mention of the pinhole camera was by the Chinese philosopher Mo-Ti.
He formally recorded the creation of an inverted image (an image that is rotated by
180 degrees) formed by light rays passing through a pinhole into a darkened room.
~350 BC Aristotle (Greece, 384-322 BC) understood the optical principle of the camera
obscura. He viewed the crescent shape of a partially eclipsed sun projected on the
ground through the holes in a sieve, and the gaps between leaves of a plane tree.
~300 BC Euclid (Alexandria). In his Optica he noted that light travels in straight lines and
described the law of reflection.
965-1020 Ibn-al-Haitham (Basra, Iraq) used spherical and parabolic mirrors and was aware of
spherical aberration (a lens or mirror defect in imaging). He also investigated the
magnification produced by lenses and atmospheric refraction. He gave a full account
of the principle of the pinhole camera including experiments with five lanterns
outside a room with a small hole.
1490
Leonardo Da Vinci (Italy) gave two clear descriptions of the pinhole camera in his
notebooks. Many of the first camera obscuras were large rooms like that illustrated by
the Dutch scientist Reinerus Gemma-Frisius in 1544 for use in observing a solar
eclipse.
1558
Giovanni Battista Della Porta (Italy), in his book Magiae Naturalis, recommended the
use of a camera with a converging lens as a drawing aid for artists.
1604
Johannes Kepler (Germany). In his book Ad Vitellionem Paralipomena, Kepler
explained vision as a consequence of the formation of an image on the retina by the
lens in the eye and correctly described the causes of long-sightedness and shortsightedness.
1608
Hans Lippershey (Netherlands) constructed a telescope with a converging objective
lens and a diverging eye lens.
1609
Galileo Galilei (Italy) constructed his own version of Lippershey's telescope and
started to use it for astronomical observations.
1611
Johannes Kepler (Germany). In his Dioptrice, Kepler presented an explanation of the
principles involved in the convergent/divergent lens microscopes and telescopes.
4
1647
B Cavalieri (Italy) derived a relationship between the radii of curvature of the
surfaces of a thin lens and its focal length.
1668
Isaac Newton (England). As a solution to the problem of chromatic aberration (image
defects related to color) exhibited by refracting telescopes, Newton constructed the
first reflecting telescope using mirrors as he believed that chromatic aberration could
never be eliminated by lenses.
1733
Chester More Hall constructed an achromatic compound lens using components made
from glasses with different refractive indices.
1873
Ernst Abbe (Germany) presented a detailed theory of image formation in the
microscope.
1953
Frits Zernike (Netherlands) won the Nobel Prize in Physics for his invention of the
phase contrast optical microscope.
1990
The Hubble space telescope was positioned in a low Earth orbit on 25th April.
Everyday examples of images
At the movie theater, film from a movie reel is imaged onto the large screen for all to see.
A camera, film or digital, is a typical example of an instrument that forms images of objects.
The image is recorded on film or an electronic detector. You see the result of this image in a
photograph or the digital image on a display. The most familiar imaging instrument is the eye.
When you look at a car on the street, an image of the car, as well as the rest of the scene, forms
on the back of your eye. Your eye is a biological lens and a detector, and is constantly forming
images.
Applications / engineering
Standard applications of imaging are eyeglasses, magnifying glasses, camera lenses, telescopes,
and microscopes. All of these applications are also taken to the extreme. Instead of eyeglasses,
the cornea of the eye can have custom correction with LASIK surgery using a laser. Professional
camera lenses are nearly fully automated and have excellent resolution. The Hubble telescope
circles the earth in space to avoid problems caused by the atmospheric absorption of certain
wavelengths of light and turbulence. There are optical microscopes that can see objects
embedded in human tissue at shallow depths.
An example of a magnifying glass is shown in Figure 5. A positive lens can magnify an object
when the object is close enough to the lens that it is within the lens’s focal length.
5
Virtual
Image
Object
focal length
of lens
Figure 5: Simple magnifying glass forms a magnified virtual image of the object.
A telescope works by magnifying the range of angles of the rays from a distant object entering
the objective of the telescope compared to the angles of the rays leaving the ocular. This is to
say that if there were no telescope, the angles of rays entering your eyes would be the same
angles of the rays entering the objective of the telescope and there is no magnification of the
image in your eye. With the telescope, the rays leave the telescope at larger angles and therefore
provide a larger image on the retina in the back of your eye.
Objective
Ocular
Real
Image
focal length
of Objective
focal length
of Ocular
Figure 6: Keplerian Telescope. The angle of rays entering the objective is small compared to the angle of
rays leaving the ocular and this provides the magnification for the eye. The magnification is also the ratio of
the objective focal length to the ocular focal length. A magnified view of a distant object is formed on the
back of the eye when the viewer looks through the telescope and the image appears inverted.
Ray Diagrams
To trace rays through a “thin” lens you can follow two or three rays through the lens (see figure
7). A ray that leaves an object and traveles parallel to the optical axis is refracted by the lens
through the rear focus F’(Ray 1), which is at a distance from the lens of f, also known as the
focal length of the lens. A ray that heads towards the center of a “thin” lens is unchanged in its
direction (Ray 2). A ray that passes through the front focus F is refracted parallel to the optical
axis (Ray 3). Notice that when the object is moved closer to the front focus F the distance to the
image increases and the image size becomes larger. The reverse is also true.
Object
1
F’
2
F
Optical
Axis
Image
3
3
1
f
f
6
2
Object
1
Optical
Axis
F’
2
F
1
3
2
f
f
3
Figure 7
7
Image
Imaging Demonstrations
Pinhole camera (also known as stenoscope or camera
obscura)
Materials Needed
-
Can with clear (semitransparent, translucent) plastic lid. (Wegmans brand coffee or peanuts
are good and cheap. The coffee comes also in big cans.)
Black or dark colored cardboard
Scissors
Scotch tape
Small nail and hammer
Aluminum foil
Pin
Procedure
1. With a small nail, make a hole at the center of the bottom of the can about 1 to 2mm in
diameter.
8
2. Remove lid. Cut a strip of dark cardboard to fit inside the can. Fix it inside, so it covers the
inner wall, in order to prevent light hitting these walls from reflecting onto the screen.
cardboard
3. Put the lid back on.
4. Tape a piece of cardboard around the can, forming a cylinder of about two or three times the
length of the can, such that the bottom of the can is at the bottom of the cylinder. Add tape
joining the can’s bottom to the cardboard, to block any gap. The cardboard helps preventing
any outside illumination from interfering with the viewing of the image.
tape
9
5. Cut the upper end of the cylinder, so that it fits your face comfortably, without letting much
light in.
6. Point your camera towards a bright object (through a window on a sunny day, a lamp, etc.)
and you will see an inverted image (object is rotated 180 degrees) projected in the plastic lid.
10
7. The image can be viewed better if you block any light that might be entering through the
cardboard. You can, for example, cover the cardboard tube with aluminum foil.
8. If the image is not bright enough, you can make the hole a bit bigger. This will cause,
however, the image to become blurrier. If you want to make the hole smaller to reduce the
blurriness, you can tape a piece of aluminum foil in front of the hole, and then with a pin
make a smaller hole.
11
Explanation
All points of the objects that we can see emit or scatter light in many directions. This light travels
in straight lines called rays. What the pinhole camera does is to select only one “ray” from each
part of the object. These rays go through the hole, and then hit the plastic lid, which works as a
screen, forming an upside-down image. This image can be hard to see because of the small
amount of light coming through the hole.
Useful information
For more information on the history of the pinhole camera and directions for building more
sophisticated models, see the following websites:
http://brightbytes.com/cosite/cohome.html
http://www.pinhole.org//make/build.cfm
http://www.howstuffworks.com/question131.htm
http://www.exploratorium.edu/light_walk/camera_todo.html
http://www.kodak.com/global/en/consumer/education/lessonPlans/pinholeCamera/
http://www.thenakedscientists.com/HTML/content/kitchenscience/exp/pinhole-camera/
12
Flashlight illumination as a sum of images
Materials Needed
-
Flashlight with smooth (not segmented) reflector
Piece of cardboard with small hole
Procedure
1. Illuminate the wall or a screen with your flashlight. The bright spot will look something like
this:
13
2. This bright spot is really many overlapping images of the filament inside the bulb. To “single
out” one of these images, place a piece of cardboard with a small hole in front of the lamp, so
that the hole is not centered but towards one side. You will then see on the wall or screen a
projection of the filament:
3. If you move the hole around, the perspective and size of the filament will change, giving the
illusion of a filament rotating in 3D . The total bright spot of the lamp is just a superposition
(or sum) of all these images (i.e. perspectives) of the filament.
Explanation
Again, we have the pinhole camera effect. This time, the image is formed by rays that leave the
filament, reflect at the reflector, and go through the hole towards the wall. When you change the
position of the hole, the apparent point of view of the filament changes.
14
Lens camera (and projector)
Materials Needed
-
Converging lens with focal length of about 10cm.
Can with clear (semitransparent) plastic lid. (Wegmans brand peanuts 10 oz, for example.)
Two yogurt containers (Size 32 oz)
Scissors
Can opener
Scotch tape
A second plastic lid (or white plastic bag), for projector
Bright flashlight, for projector
Procedure
1. With the can opener, remove the bottom of the can.
2. Cut also the bottom of one of the yogurt containers.
15
3. Push the upside-down can firmly into the top of this yogurt container.
4. Make a hole at the center of the bottom of the second yogurt container. This hole should be a
bit smaller than the lens.
5. Cover the sides and bottom of this outside container with dark cardboard or aluminum foil.
16
6. Tape or glue the lens at the bottom of the container, centered at the hole.
7. Insert the yogurt container with the can into the one with the lens.
8. The camera is ready. You can focus objects at different distances by sliding the inner
container in and out of the outer one. The image is projected onto the plastic lid. Because the
lens collects much more light than the pinhole, the images are much brighter.
17
9. You can also use your camera as a projector. Pull the inside container out, and stick a slide to
the plastic lid. Put this container back inside the other one.
10. Put a second translucent plastic lid (or a few layers of white plastic bag) on top of a
flashlight, in order to make the illumination diffuse.
18
11. Place the flashlight next to the viewer of the camera.
12. Turn the lamp on, and project the image onto a wall or screen in a dark room. Again, you can
focus the inverted image by moving the second container with respect to the first one.
19
Explanation
Lenses bend light, due to refraction. Converging lenses can collect many rays coming from a
point on a bright object and bend them such that they cross at a point on a screen, forming an
image. Because many rays are used instead of just “one” (that is, very few) as in the case of the
pinhole camera, the images are much brighter and easy to see. The diagrams below show a
comparison of the pinhole camera and the lens camera. The image in the second case is brighter
than the first one by as many times as the area of the lens is larger than that of the pinhole.
20
Forming an image with a concave mirror
Materials Needed
-
Small concave (magnifying) make-up mirror, available at any drugstore or supermarket for
about $3. These mirrors usually have two sides, one flat and one concave. Only the concave
side works.
-
White paper or white wall.
Window, TV or bright computer monitor.
Procedure
1. Hold the mirror in front of both the window (or monitor), with the concave side facing it.
Move it until you form an image of the outside (or the image in the monitor) onto the wall or
a piece of paper.
21
Explanation
A concave mirror, like a converging lens, can bend rays to make them converge at a point, as
shown in the diagram.
22
Forming an image with a soda bottle
Equipment
-2 liter soda bottle
-Scissors
-Water
-Overhead lighting
-White paper
Procedure
1. Use scissors to cut a roughly circular piece of the bottle from just below the neck. You
should be cutting where the bottle is curved both towards the neck and around the bottle, so
that the piece you cut out forms a shallow bowl shape.
2. Place a white piece of paper on the floor (somewhere where you won’t mind spilling a little
water).
23
3. Pour a little water into the bowl-shape and slowly move it towards the piece of paper. Stop
when it is about 15 cm (roughly 6 inches) from the paper. You should see an image of the
overhead light projected on the paper. If you’re using an incandescent light like I was, you’ll
see a bright spot which is a slightly-blurred image of the light bulb.
4. Now, get a small object, such as a pen, and place it on the piece of paper. Instead trying to
form an image of the overhead light, try looking through the bowl at the pen. You should
notice that the bowl is acting much like a magnifying glass.
Explanation
Recall the definition of a lens from the introduction. It has at least one curved side, and
in order to form real images (such as the light on the paper) it must be thicker at the center than
at the edges. When you first cut out the bowl-shape it was curved, but the plastic was equally
24
thick in the center as at the edges. However, when you poured water into the bowl, the depth of
the water was thickest in the center and thinner towards, the edges, which allows the bowl-withwater to bend light rays and act like a lens. The technical term for such a lens is plano-convex,
since the top side is a flat plane and the bottom is curved outwards (convex).
When you focus the light from the ceiling onto the paper, the lens is bending the light
rays from each point on the light bulb so that they all arrive at the same point on the piece of
paper, as illustrated here.
25
When you instead look through the lens at an object, the lens bends the light rays so that
they seem to be coming from a much larger object than they actually are. This object seems to
be on the other side of the lens, and it is what is called a virtual image.
More information
This demonstration was adapted from :
http://www.thenakedscientists.com/HTML/content/kitchenscience/exp/make-a-camera-from-alemonade-bottle/
http://en.wikipedia.org/wiki/Concave_lens
26
Single lens imaging Demonstration
Equipment
Lens (small plastic convex, obtained from OSA Educators’ Day or another small size positive
lens)
Flashlight
Clear plastic diffuse bag (Ex. Wegmans plastic grocery bag)
Scissors
Scotch tape
Poster tack or double sided tape
Folder
Styrofoam Cups (Quantity 1 or more, Size 20oz)
Permanent markers of various colors
Yardstick or meterstick
Binder Clips (2 large)
Graph Paper (1 sheet)
Ruler
Set up and assembly
1. Tape yardstick down to table using Scotch tape leaving one long side untaped to provide an
optical rail.
2. Look through the lens at an arms length out a window and make sure that the image you see
is inverted. Take the plastic lens and use poster tack or double sided tape to position it on the
table, next to the ruler, as demonstrated in Figure 1. (If your flashlight is taller than the lens,
you may have to prop the lens up on something such as a notebook in order to form an image
properly). Ensure that the orientation of the lens is square to the table and optical rail by
hand. If the image is not inverted please find a shorter positive focal length lens.
Plastic Lens
Poster tack
Taped down meter or yardstick
Figure 1
27
3. Cut the bottom out of another 20oz Styrofoam cup. Cut a 4” diameter circle out of a
colorless diffuse plastic bag. Tape the plastic over the bottomless cup such that the plastic is
taut and there are no wrinkles in the plastic over the hole. Using various color permanent
markers, draw a graphic or graphics onto the plastic. See Figure 2. These graphics become
the object that is imaged by the lens. Measure and note the size of the graphics with the
ruler.
Various colored graphics on plastic
stretched over bottomless Styrofoam cup.
Figure 2
4. Cut another 4” diameter circle out of a colorless diffuse plastic bag again. Tape the plastic
over the front of the flashlight such that the plastic is taut and there are no wrinkles in the
plastic over the flashlight. Place flashlight next to the optical rail so that it shines through the
lens. Then place the cup with graphics over the end of the flashlight. Place the
flashlight/cup assembly on the table, next to the optical rail, and center the flashlight and
cups with the lens. See Figure 3. Position the cup with graphics about 305mm (or 12”) from
desired image plane (say at beginning of optical rail).
Figure 3
5. Measure grid spacing on graph paper with ruler and note spacing. Fold sheet of graph paper
in half to make the paper roughly 8.5” by 5.5”, or tape it to a piece of thick paper. Clip two
large binder clips on either edge of the graph paper and position assembly at the desired
28
image plane (say at beginning of optical rail) and position the paper roughly centered on the
axis of the lens.
Demonstration: Single Lens Imaging with a fixed object to screen distance
1. Turn flashlight on and adjust the position of the lens against the optical rail and slide lens
next to your object (cup with graphics). Then move the lens away from the object, ensuring
that the lens slides against the optical rail, until a sharp image is formed. See Figure 4a.
Count the number of grid squares for the portion of the image. This is the first image with
the lens at the first position. Compare the image size to the object size. Please note that if
the first image is out of focus or is never formed then increase the distance between the
object and the screen by approximately 100 - 200mm or (4 -8”) and repeat this step.
Figure 4a
29
2. Continue to move the lens away from the object until a second sharp image is obtained. See
Figure 4b. Note the size of this image by counting the grid squares and compare that to the
object. This is the second image with the lens at the second position.
Figure 4b
Follow up discussion/questions
-
Why are the images inverted?
-
What are the magnifications of the first image at the first lens position and the second image
at the second lens position? Are the magnifications the inverse of one another? Discuss
some ideas of why this may possibly be the case?
-
If an unknown focal length lens is used: What is the focal length of the lens?
-
If the object to screen distance is narrowed until the [object to screen] = [4 times the focal
length of lens] and the demonstration repeated, why does eventually only one image form?
30
Also why when the object to screen distance is narrow enough ([object to screen distance] <
[4 times the focal length of lens]) no images are formed?
Deeper explanation:
An interesting characteristic of using a thin lens of focal length f to project an object on to a
screen at a fixed distance d from the object is that there are two possible positions for the
projection lens to form real images when d ≥ 4f. It can also be shown that these two possible
positions have images that have inverse magnifications from one another. If the focal length of
the lens is unknown, by measuring the size of the object and one of the images, to determine the
magnification, and measuring the object to lens distance, the focal length of the lens can be
found. Figure 5 and Figure 6 illustrate a thin lens at the two positions that produce sharp images.
Lens
Position 1
Object
Image 1
S1o
S1i
d
(fixed distance)
Figure 5: Projection lens of focal length f at position 1 where S1o is the distance from the object to the thin
lens at position 1 and S1i is the distance from the lens at position 1 to the image and d is the sum of S1o and
S1i.
Lens
Position 2
Object
Image 2
S2o
S2i
d
(fixed distance)
Figure 6: Projection lens at position 2 where The distances S2o and S2i correspond to the to the object and
image distances from the lens at position 2 respectively, and the sum of S2o and S2i is d.
To find the distances involved in forming an image with a thin lens we can begin with the
lensmaker’s formula:
31
1
1
1
+
=
So Si
f
(1)
where the So is the object to lens distance and Si is the lens to image distance and are both
positive. This is rearranged:
So =
Si f
Si − f
(2)
The sum of So and Si are equal to the fixed object to screen (image) distance d:
d = So + Si
(3)
(3)
Rearranging equation 3 and substituting Si into equation 2 and solving for So we obtain:
d ± d 2 − 4df
So =
2
(4)
This provides for two real image solutions provided that f ≤ d/4. We can then represent lens
position 1 and position 2 from the object respectively as:
d − d 2 − 4df
S1o =
2
S 2o =
(5)
(5)
d + d 2 − 4df
2
(6)
To determine the magnification relation between image 1, determined from lens position 1, and
image 2, determined from lens position 2, we use the following relations:
m1 = −
S1i
S1o
m2 = −
S 2i
S 2o
m1 ⋅ m2 =
S1i S 2 i
⋅
S1o S 2 o
(7)
(7)
(8)
(9)
Where m1 is the magnification of image 1, and m2 is the magnification of image 2. The negative
sign in front of each equation indicates that the image is inverted. Solving equation 1 for S1i and
S2i, in a similar manner as was done in equation 2, gives:
32
S1i =
S1o f
S1o − f
S 2i =
S 2o f
S 2o − f
(10)
(10)
(11)
Substituting equations 10, 11 and then 5, and 6 into equation 9 gives the relation between
magnifications as:
m1 =
1
m2
(12)
thus showing that the magnifications of image 1 and image 2 are the inverse of one another.
If the focal length of the lens is unknown, it can be found when the magnification of one of the
images is known and the distance from the object to the lens is known (or distance from the lens
to the image is known). In addition to equation 7 and 8, the magnification of the image can be
defined as the following:
m=−
yi
S
=− i
yo
So
(13)
(13)
where yi is the size of the image and yo is the size of the object and both sizes are positive values
and the negative sign indicates an inverted image. This is equivalent to the magnification as
defined in equation 7 and 8. Once the magnification is found by measuring yi and yo, and
knowing that:
(14)
S i = −m ⋅ S o
(14)
then substituting equation 14 into equation 2 allows one to solve for the focal length f below:
f =
So ⋅ m
m −1
(15)
(15)
keeping in mind that m is negative as defined above when working with real images and a single
lens.
33
Specific Example
Consider a lens that has a focal length of 100mm and we make the object to image distance of
450mm. Substituting the above values into equation 5 and 6 to find the object to lens distance at
position 1 and position 2 provides:
450mm − (450mm) 2 − 4 ⋅ 450mm ⋅ 100mm
S1o =
= 150mm
2
S 2o =
450 mm + ( 450 mm ) 2 − 4 ⋅ 450 mm ⋅ 100 mm
= 300 mm
2
Utilizing equation 3 to find S1i and S2i gives:
S 2 i = 450mm − 300mm = 150mm
S1i = 450mm − 150mm = 300mm
Substituting the above information into equations 7 and 8 yields:
m1 =
− 300mm
= −2
150mm
m2 =
− 150mm
1
=−
300mm
2
Both images are inverted with image 1 being 4 times the size of image 2. Figure 7 illustrates this
example.
34
Lens
Position 1
Object
Image 1
(a)
150mm
300mm
Lens
Position 2
Object
Image 2
(b)
150mm
300mm
Figure 7: (a) Projection lens with a 100mm focal length at position 1 where the distance from the object to
the thin lens at position 1 is 150mm and the distance from the lens at position 1 to the image is 300mm with
image 1 having a magnification of –2. (b) Using the same projection lens in (a) at position 2 where the
distance from the object to the thin lens at position 1 is 300mm and the distance from the lens at position 1 to
the image is 150mm with the image 2 having a magnification of –1/2.
Useful information
For more information on imaging please see the listed references below.
-
Frank L. Pedrotti, S.J. and Leno S. Pedrotti, “Introduction to Optics, Second Edition,” (Prentice-Hall,
Inc. 1993)
http://www.hazelwood.k12.mo.us/~grichert/optics/intro.html (Optics Bench - A lot of fun!)
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Optical system demonstration
Anatomy of a camera
Equipment
Kodak FunSaver35 Camera
One flathead screwdriver from eyeglass repair kit
(or other similar tool to pry the camera open)
Two pen caps
Set up and disassembly
1. Remove camera from packaging. Slowly and gently peal off front and back label with
fingers. See Figure 1 to see camera with label.
Button to charge flash
Figure 1: Camera with label
Caution: Before step two, please note that there is a AA size battery that charges the capacitor
which then powers the flash. If you do not know if the flash is charged (if the button to charge
the flash was inadvertently pushed), then take a picture with the camera and let sit for 30 minutes
to avoid risk of an electrical shock.
2. Pry open the camera using a small flathead screwdriver and pen caps. This is done by
wedging the screw driver and pen caps under the top and bottom of the camera and prying
open the left and right sides of the camera as indicated in a series of pictures in Figure 2 on
the top, bottom, left and right sides. To facilitate opening the camera, once the screwdriver
has pried open the top of the camera, slide in a pen cap before removing the screwdriver and
then remove the screwdriver when pen cap is in place. Then repeat this last step for the
bottom as shown in Figure 2a and b. Now pry open in left side (camera facing you) with the
screwdriver only as shown in Figure 2c and then pry open the right side with the screwdriver
only as shown in Figure 2d.
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Wedge screwdriver
and first pen cap
here
Wedge screwdriver
and second pen cap
here
(a)
Pry open left side with screw driver
(b)
Pry open right side with screw driver
(c)
(d)
Figure 2: (a) Top view (b) bottom view (c) left view (d) right view
3. Once the camera is open, remove the AA size battery and film. Figure 3 shows the camera
opened, but with the film and battery still in place. Figure 4 shows the camera with battery
and film removed.
Front and back case
Battery
Film
Figure 3: Camera is first opened and lying on its face
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Figure 4: Camera with battery and film removed
4. Flip camera such that it is facing you and identify the optical components shown in Figure 5.
Gently push down and turn counter-clockwise the gray retaining ring holding the camera lens
and remove the retaining ring and lens. Remove the lens for the flash by pulling and
wiggling it out. Next, tilt the camera such that you are looking at the top of the camera and
remove the view finder by gently pulling it up and away from the camera. A view of the
components is shown in Figure 6.
View Finder
Lens for Flash
Camera Lens
Retaining Ring
Figure 5: Exposed camera highlighting optical components
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Figure 6: Exposed camera with optical components removed
Exploration
1. Explore the optics. Find bright light sources and image them on to paper, tables, walls, etc.
Roughly determine the focal length of each optic and see how they differ.
The camera lens provides a sharp image on the film plane. The lens covering the flash is
very interesting. It has a simple cylindrical lens on the outside and a cylindrical lens in on
the inside in the other dimension. The view finder has four optical components. The
positive lens is where your eye looks through and the negative lens faces out to your scene
that you are taking a picture of. Together, they demagnify the view. The Light Pipe guides
light from the red LED, when the flash is charging, to the outside edge of the camera. See
Figure 7
Positive lens
of view finder
Short focal length lens provides
magnification for indicator for number
of pictures left
Negative lens of view finder
Light Pipe for LED to
indicate when the
flash is fully charged
Figure 7: Optics components of camera
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2. Place all of the optics back on the camera as they were previously in Figure 5. Place a piece
of Scotch tape along the center back of the camera where the film would be. Now point the
camera at a distant indoor light source or out a window to see the inverted image on the tape.
See Figure 8.
Figure 8: Scotch tape in film plane
3. Explore the mechanical function of the camera. Place the camera down on its face. Turn the
gray wheel with spokes where the film would be and this prepares the camera to take a
picture. See figure 9. Press the gray button on the top of the camera to snap the shutter open
briefly.
Turn this wheel here
Figure 9
For those who wish to further investigate the mechanics and electronics, the camera will further
disassemble allowing for a deeper understanding of those functions.
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Follow up discussion/questions
-
Is the image inverted on the film plane? Why?
-
Since the shutter speed is always the same for this camera, what does that tell you about
using the camera outdoors on a sunny day versus indoors using the flash?
-
Why does the view finder demagnify the view?
How it works
There are four essential elements in a single-use-camera. The lens, the film, shutter, and camera
body as shown in Figure 10. The lens is already set at the correct distance to form an image on
the film. The film is chemically altered by the light and records the image. The camera body
keeps the inside of the camera dark so as to not have any extraneous light expose the film. The
length of time that the shutter is open, typically a fraction of a second with single-use-cameras,
then controls the amount of light that can expose the film. The old advertising slogan of Kodak
still holds for this camera. “You press the button, we do the rest”.
Camera body
Shutter
Film
Inverted image of distant scene
Lens
Figure 10: Essential elements of a single use camera
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Useful information
For more information on how cameras work, see the references below.
-
-
David Falk, Dieter Brill, and David Stork, “Seeing The Light: Optics in Nature, Photography, Color,
Vision, and Holography,” (John Wiley & Sons, Inc. 1986)
http://entertainment.howstuffworks.com/camera.htm/printable
http://electronics.howstuffworks.com/digital-camera.htm/printable
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