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Are teachers aware of a screwy diagram that appears widely in popular
books and children's science textbooks? I first noticed it in a major
grade-school text. After becoming "sensitized" to its existence,
I started noticing it in many other texts, popular science books,
newspapers, etc. Here is a crude version:
...that objects must always be smaller than the lens in order to "fit
through" the aperture. (It does not show how a tiny lens can capture a
huge object.)
...that when the screen is moved closer to the lens, the inverted image on
the screen will contract to a point, then become erect. In reality,
as the screen is moved closer, the image shrinks and becomes
increasingly blurry, and never becomes erect at all.
...that there is a special point *between* the lens and the screen where
all the light comes to a focus. In reality, light comes to a focus
*at* the screen)
...that the distance between the lens and screen doesn't affect the
sharpness of the image. In reality, any changes in the lens/screen
distance will produce different amounts of blur.
...that light from an object takes the form of parallel rays, as if
there were a full-sized "phantom object" which flys from the object to
the lens.
...that a camera based upon a simple lens is fundamentally different
than a pinhole camera. In reality, a simple 1-lens camera is very
similar to a pinhole camera. The lens simply allows the "pinhole" to
be made large without causing the image to become blurry.
The faulty diagram has direct bearing on the whole "science misconception"
area which is attracting so much attention recently. Misconceptions are
formed in our early years, and then they create serious barriers to
learning during later schooling. Early concepts are a stumbling block for
many of us, and probably are a major force for turning people away from
science classes. But note that some misconceptions do not occur
naturally. They are specifically taught by faulty textbooks.
Suppose that students encounter this faulty diagram and then find optics
difficult to understand forever after. If true, then any books which
contain the diagram do actual harm. And the number of books is not small
(see below.)
I've seen this diagram in about twenty five books now, and in quite a few
newspaper and magazine articles. In an anti-evolution article, it was
offered as proof that eyes could not function in intermediate states of
evolution. In an Am. Journal of Physucs paper by Goldberg and McDermott
about student
misconceptions, the college freshmen participating in the study were
obviously basing many of their naive optics notions on just this diagram.
A number of gradeschool science texts use the diagram to explain near- and
far-sightedness. It appears in classroom posters which purport to explain
eyes. It even appears on the cover of a college-level photography text!
I fear that it has become firmly embedded in the popular imagination. I
suspect that it also is spreading from textbook to textbook like some sort
of infection.
One point of this message is to find out if instructors and authors are
aware of these "communicable misconceptions" which have spread from book
to book, and even now are being used to misinform the young. There are a
number of other examples out there as well, both in the form of diagrams
and written explanations.
By the way, here are a couple of corrected versions of the diagram...
This one is appropriate for explaining how images are formed:
The one below shows how light from the object is focussed to create a
sharp image:
Below is a diagram that combines the features of the two diagrams above.
It shows how the light from one point on the object is focused to one spot
on the screen, and it also illustrates the "camera obscura" principle:
where the lens behaves like a pinhole camera.
Also note that each individual ray in the "bad" diagram is correct.
However, the rays in the diagram below are also correct, yet the diagram
certainly does not explain how cameras or eyes work! Even if each ray is
correct, the entire diagram can be wrong.
CHILDREN'S SCIENCE BOOKS
"How It Works, Vol II" 1974 p191-194
TEXTBOOKS AND EDUCATIONAL MATERIAL
"Physical Science" Prentice-Hall, 1988 p569
OTHER
"Academic American Encyclopedia" 1986, entry under "eye"
F.M. Goldberg and L. C. McDermott, AN INVESTIGATION OF STUDENT
UNDERSTANDING OF THE REAL IMAGE FORMED BY A CONVERGING LENS OR CONCAVE
MIRROR, Am. J. of Phys. 55 (2) Feb. 1987 pp108-119.
PROCEEDINGS OF THE 2nd INTL SEMINAR ON MISCONCEPTIONS AND EDUCATIONAL
STRATEGIES IN SCIENCE AND MATHEMATICS, VOL 1-3 1987 Cornell U., Ithaca NY
Mario Iona, WHY JOHNNY CAN'T LEARN PHYSICS FROM TEXTBOOKS I HAVE KNOWN
Millikan Award Lecture, Am J. Phys. 55 (4) Apr 1987 pp299-307
Mario Iona, HOW SHOULD WE SAY IT? Series of columns in The Science
Teacher, 1970-1972
Mario Iona, WOULD YOUR BELIEVE? Series of columns in The Physics Teacher
Teacher, 1970-1972
Fig. 1
__________________ /\__ __ - |
/^\ / \ --__ __-- |
| | | --__ __-- |
| | | --__ |
| | | __-- --__ |
| __________________| |__-- --__ |
\ / \|/
\/
object lens screen
The above diagram is faulty. It purports to explain how cameras and eyes
form images. Yet it teaches quite a number of incorrect concepts. It
wrongly suggests:
...that if half the lens is covered, half of the image will vanish. In
reality, if half of the lens is covered, the image will become half
as bright, but no part of the image will be missing.
See figures 2 and 3 for correct versions.
Fig. 2
___--- |
/\ ___--- |
/|\ ---___ / \ ___--- |
| ---___ | | ___--- |
| --| |- |
| __| |_ |
| ___--- | | ---___ |
| __--- | | ---___ |
| -- \ / ---___ |
\/ ---__ \|/
object lens screen
It shows that a simple-lens camera is fundamentally *similar* to a pinhole
camera. It correctly shows that the image projected on a screen will
shrink in size as the screen is moved towards the lens, and it shows why
an image is upside-down.
Fig. 3
|
__ /\ ___ |
/|\ __-- / \ ----___ |
| __-- | | ---____ |
| __-- | | ---___ |
|-==__ | | ___=== |
| --__ | | ____--- |
| --__ | | ___--- |
--__ \ /___---- |
\/ \|/
object lens screen
It shows why the image becomes sharp at one special distance, why a large
lens gathers more light than a small lens, and it shows why a large image
can "get through" even a tiny lens.
Fig. 4
/^\----_____
| ---___ -----_____
| --___ -----_____
| --___ ---- /\ -_ |
| --___ / \ -_ |
| --___ | | -_ |
| --___ \ / -_ |
| \/---------=\|/
|
Lens Screen
Object
Keep in mind that these diagrams are intended for children. Any optics
textbook will obviously use much more precise and complex diagrams.
Fig. 5
__ __ - /\---------------- |
/^\ --__ __-- / \ |
| --__ __-- | | |
| --__ | | |
| __-- --__ | | |
| __-- --__ \ / |
| -- \/________________ \ /
object lens screen
THIS ONE'S JUST AS BAD AS FIG. 1
Some books which contain the bad diagram:
"How It Works... the Telescope and Microscope" 1971 p11
"Light and Radiation" 1968 p30
"Eye and Brain" 1973 p23
"Light and Vision" 1966 p35
"First book of Light" 1962 p48
"Understanding Light" 1960, p102,106
"The Story of Light" 1952, p23,33-37
"Light and Sight" 1963, p49
"Optics: Light for a New Age" 1987
"Holt Science" fifth grade text, 1984 p130
"The New Exploring Science" 1982 p172
Silver-Burdett "Science" instructor's workbook p69
"Elementary School Science and How to Teach It" 1984 p561
"Teaching Children Science",1982 p352
"Teaching Science Through Discovery" 3rd ed., 1985 p505
"Physics for Scientists and Engineers" 2nd ed, 1986
"Perception" 1984 p2
"Photography" 1984 (cover, and several diagrams)
"A Sourcebook of Elementary Science" 1971 p244
Carolina Biological Supply, transparency 50-6950
"Encyclopedia Americana" 1986, Vol E, p812
"Science and Technology Illustrated" Ency. Brit. 1983, under "Lens"
"Physics in Everyday Life" 1979 p239
"LIFE Science Library, Light and Vision" 1966 p35, p54
"Life Library of Photography, The Camera" 1970 p64, p77
"Time-Life Inc "Light and Film" 1970 (frontspiece)
"Eye and Brain" 1973 p23
Some Misconception Resources:
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