A LENS MISCONCEPTION
William J. Beaty 1994
Email discussion
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:
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. Wrong! In reality, if half of the lens is covered, the entire image will become half as bright, but no part of the image will be missing. (This is a very important concept in understanding how cameras actually work.)See figures 2 and 3 below for more correct versions....objects must always be smaller than the lens in order to "fit through" the aperture. Wrong. The diagram does not explain how a tiny lens can capture a photograph of a large object.
...when the screen is moved closer to the lens, the inverted image on the screen will first contract to a point. Then as the screen moves further, the image will become erect. Wrong and wrong. In reality, as the screen is moved closer to the lens, the image both shrinks and becomes increasingly blurry, and never becomes erect at all.
...there is supposed to be special point *between* the lens and the screen where all the light comes to a focus. Wrong. In reality, light comes to a focus *at* the screen.
...the distance between the lens and screen supposedly has no effect on the sharpness of the image. Wrong In reality, any changes in the lens/screen distance will produce various amounts of blur.
...the light from an object supposedly takes the form of parallel rays, as if there were a full-sized "phantom object" which flys from the object to the lens. Nope. Unlike in the diagram, the rays from the object are actually crossing each other.
...a camera based upon a single basic lens is fundamentally different from a pinhole camera. Wrong. In reality, a simple 1-lens camera is very similar to a pinhole camera. The lens simply allows the "pinhole" to be made quite large without causing the image to become blurry.
The above faulty diagram has direct bearing on the topic of "science
misconceptions" which has attracted 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. Instead they're being taught to us by faulty
textbooks. Suppose that students encounter this misleading diagram and
then find optics difficult to understand forever after. If this occurs,
then any books which contain the diagram are doing 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, the
diagram 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 currently are misinforming children. There are a number of
other examples out there as well, both in the form of diagrams and written
explanations.
Here are a couple of corrected versions of the diagram...
This one is appropriate for explaining how images are formed:
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
a real image upon a screen is upside-down.
The one below shows how light from the object is focussed to create a
sharp image:
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.
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.
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.
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.
Fig. 5
__ __ - /\---------------- |
/^\ --__ __-- / \ |
| --__ __-- | | |
| --__ | | |
| __-- --__ | | |
| __-- --__ \ / |
| -- \/________________ \ /
object lens screen
THIS ONE'S JUST AS BAD AS FIG. 1
Some books which contain the Fig. 1 bad diagram:
CHILDREN'S SCIENCE BOOKS
"How It Works, Vol II" 1974 p191-194
"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
TEXTBOOKS AND EDUCATIONAL MATERIAL
"Physical Science" Prentice-Hall, 1988 p569
"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
OTHER
"Academic American Encyclopedia" 1986, entry under "eye"
"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:
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
