A LENS MISCONCEPTION
William J. Beaty 1994
From: billbeskimo.com (William Beaty)
Subject: A misconception spread by texts
Date: Sat, 3 Dec 1994 15:14:27 GMT
Are people aware of the presence of a screwy diagram that appears
widely in popular books and children's textbooks? I noticed it
in a popular grade-school text, and then started noticing it in
many other texts, popular science books, newspapers, etc. Here is
a crude version:
______________ /\__ __ - |
/^\ / \ --__ __-- |
| | | --__ __-- |
| | | --__ |
| | | __-- --__ |
| ______________| |__-- --__ |
\ / \|/
\/
object lens screen
The diagram purports to explain how cameras and eyes form images. Yet it
implies many incorrect ideas: that the lens/object distance doesn't affect
the image, that the object must be smaller than the lens in order to
"fit," that the inverted image on the screen will become erect if the
screen is moved close to the lens, and that lens cameras are basically
different than pinhole cameras.
I've seen this diagram in about twenty separate places now, including the
cover of a text on cameras! In an anti-evolution article, it was offered
in support of the idea that eyes could not function in intermediate states
of evolution. In a paper by McDermott on student misconceptions, the
students participating in dialog seemed to be basing their naiive notions
about optics on the above diagram. I fear that it has become firmly
embedded in the popular imagination, and also seems to be spreading from
textbook to textbook like some sort of mind-virus.
The point of this message is to find out if instructors are aware of "communicable misconceptions" like the above diagram. There are a number of other ones out there as well, both in the form of diagrams and written explanations.
************************************************************************ William J. Beaty http://amasci.com Engineer/programmer/exhibit designer Science hobbyist page billbeskimo.com, Seattle, WA
By the way, here is a more correct version.
___--- |
/\ ___--- |
/|\ ---___ / \ ___--- |
| ---___ | | ___--- |
| ---_| |- |
| ___-| |_ |
| ___--- | | ---___ |
| __--- | | ---___ |
\ / ---___ |
\/ ---___\|/
object lens screen
--
.....................uuuu / oo \ uuuu........,.............................
William Beaty voice: bbs:206-789-0775 cserv:71241,3623
EE/Programmer/Science exhibit designer http://amasci.com/
Seattle, WA 98117 billbeskimo.com SCIENCE HOBBYIST web page
Date: Sun, 4 Dec 94 13:56:36 PST
From: R_Tim_Coslet@cup.portal.com
To: William Beaty
Subject: Re: A misconception spread by texts
> > ______________ /\__ __ - | > /^\ / \ --__ __-- | > | | | --__ __-- | > | | | --__ | > | | | __-- --__ | > | ______________| |__-- --__ | > \ / \|/ > \/ > > object lens screen
The major problem (as I see it) with this diagram is simply that
it oversimplifies things to produce a "readable" figure.
The oversimplification is that is picks a single pair of light
rays to follow, and probably NOT the best pair. But any attempt
to show on paper in a single figure ALL the relavent rays will
unfortunately produce a nearly indecypherable diagram.
The main thing that it DOES illustrate is the operation of the
lens by refraction of the light rays. This is VITAL to developing
any understanding of a lens.
> > >By the way, here is a more correct version.
> > ___--- | > /\ ___--- | > /|\ ---___ / \ ___--- | > | ---___ | | ___--- | > | ---_| |- | > | ___-| |_ | > | ___--- | | ---___ | > | __--- | | ---___ | > \ / ---___ | > \/ ---___\|/ > > object lens screen >
Hmm, not exactly "more correct", you simply picked a different
pair of light rays to follow.
Unfortunately, your pair of rays, passing so close to the center
of the lens fail to illustrate any significant refraction effects.
These ARE indeed the same rays that are used by both lenses and
pinholes to produce their images... but the advantage of a lens
is that it gets a larger aperture because the refraction
effect permits OTHER light rays to also contribute to the
image brightness.
A MINIMAL figure that I would consider acceptable to illustrate the
concepts of lenses would need to trace a dozen or so rays (including
both the rays of the original figure and those of your "more correct"
figure). Unfortunately this MAY be too cluttered for many books
to consider printing it.
R. Tim Coslet
Date: Tue, 6 Dec 1994 05:04:37 -0800 (PST)
From: William Beaty
To: R_Tim_Coslet@cup.portal.com
Subject: Re: A misconception spread by texts
On Sun, 4 Dec 1994 R_Tim_Coslet@cup.portal.com wrote:
> >billbeskimo.com wrote:
> >
> > ______________ /\__ __ - |
> > /^\ / \ --__ __-- |
> > | | | --__ __-- |
> > | | | --__ |
> > | | | __-- --__ |
> > | ______________| |__-- --__ |
> > \ / \|/
> > \/
> >
> > object lens screen
>
> The major problem (as I see it) with this diagram is simply that
> it oversimplifies things to produce a "readable" figure.
Yet it produces serious misconceptions as to how lenses work. Want to
check out the McDermott paper on student's optics misconceptions? I think
it was in '88 or '89 in AJP. The paper discusses results of pre-tests of
student understanding of lenses before they took an optics course. A
large percentage of the students predicted that when a screen behind a
lens was slid from the location of the real-image and moved toward the
lens, the image on the screen would contract to a point, then reappear
RIGHT SIDE UP. Many of them drew the above diagram to explain their
beliefs. I think this is strong evidence that the above diagram is
creating serious misconceptions in those who HAVE NOT taken optics courses
(the majority of the population.) I didn't make it entirely clear that the
above diagram mostly appears in gradeschool texts and in books aimed at
the public.
>
> The oversimplification is that is picks a single pair of light
> rays to follow, and probably NOT the best pair. But any attempt
> to show on paper in a single figure ALL the relavent rays will
> unfortunately produce a nearly indecypherable diagram.
>
> The main thing that it DOES illustrate is the operation of the
> lens by refraction of the light rays. This is VITAL to developing
> any understanding of a lens.
Good point. But shouldn't the above diagram show that the rays come
to a focus at the real image, and not somewhere in the space between
the lens and the screen?
My diagram below was offered as an equally-oversimplified but improved
view as to how a camera or eye generally works. A camera is simply an
aperature in a box (a 'pinhole'), with a lens installed in the aperature.
The diagram below is a crude explanation of where the image comes from.
The diagram above is not. The diagram below unfortunately is too
simplified, and it does not explain why the image on the screen is
blurry at some screen positions and sharp at others.
> >
> >
> >By the way, here is a more correct version.
> >
> Hmm, not exactly "more correct", you simply picked a different
> pair of light rays to follow.
Oooops! I should have called it "less misleading."
> A MINIMAL figure that I would consider acceptable to illustrate the
> concepts of lenses would need to trace a dozen or so rays (including
> both the rays of the original figure and those of your "more correct"
> figure). Unfortunately this MAY be too cluttered for many books
> to consider printing it.
Maybe something more like the one below? Oversimplified still, but
it combines both the refraction and the camera-obscura concepts
needed in any explanation.
/^\----_____ | ---___ -----_____ | --___ -----_____ | --___ ---- /\ -_ | | --___ / \ -_ | | --___ | | -_ | | --___ \ / -_ | | \/---------=\|/ |
Darn ascii art! There must be an easier way than this, or by UUE.
Those Mosaic guys should look into setting some graphics standards
for usenet.
Well, thanks much for your input. It's helping me think more clearly
about the problem.
.....................uuuu / oo \ uuuu........,............................. William Beaty voice:206 bbs:206-789-0775 cserv:71241,3623 EE/Programmer/Science exhibit designer http://amasci.com/ Seattle, WA 98117 billbeskimo.com SCIENCE HOBBYIST web page
From: dave.moore@tcbbs.cais.com (DAVE MOORE)
Newsgroups: k12.ed.science
Subject: A misconception spread by
Date: Sun, 04 Dec 94 18:49:00 -0500
WB> @FROM :billbeskimo.com
WB>Are people aware of the presence of a screwy diagram that appears
WB>widely in popular books and children's textbooks? I noticed it
WB>in a popular grade-school text, and then started noticing it in
WB>many other texts, popular science books, newspapers, etc. Here is
WB>a crude version:
WB> ______________ /\__ __ - |
WB> /^\ / \ --__ __-- |
WB> | | | --__ __-- |
WB> | | | --__ |
WB> | | | __-- --__ |
WB> | ______________| |__-- --__ |
WB> \ / \|/
WB> \/
WB> object lens screen
WB>The diagram purports to explain how cameras and eyes form images. Yet
WB>it implies many incorrect ideas: that the lens/object distance
WB>doesn't affect the image, that the object must be smaller than the
WB>lens in order to "fit," that the inverted image on the screen will
WB>become erect if the screen is moved close to the lens, and that lens
WB>cameras are basically different than pinhole cameras.
It's difficult to separate the limitations of ascii art from the point
that you're trying to make. However if one assumes near parallel rays
from an object arbitrarily far away, the object appears to be smaller
than the lenses regardless of the size. The classic example is that of
stars. The question in this diagram is why the image appears where it
does rather than left or right. What's missing are rays through the
lens center and focus to make the image position obvious.
WB>By the way, here is a more correct version.
WB> ___--- |
WB> /\ ___--- |
WB> /|\ ---___ / \ ___--- |
WB> | ---___ | | ___--- |
WB> | ---_| |- |
WB> | ___-| |_ |
WB> | ___--- | | ---___ |
WB> | __--- | | ---___ |
WB> \ / ---___ |
WB> \/ ---___\|/
WB> object lens screen
Your diagram suffers from the same problem. Try this one:
/\
/ \
| |
| |
| | ___
/|\ ----- | | ___ |
| \ ----- | | ___ |
| \ ----- | | ___ |
| \ ---- | | ___ |
| \ focus -| | focus ___ |
| .......\...........|....|___.......___................|... Center
| \ | | --- ___ |
| _______ _____\_______| |_____-- ----- |
\ | | ----- |
\ | | ----- |
\ | | ---- |
object | | ___________________________\|/___
| |
\ / real image
\/
lens
In the above: a ray from the object head passes in a straight line
through the center of the lens. Another ray from the object head passes
through the near focus and comes out of the lens parallel to the center.
The intersection of these two rays defines the image point. The size of
the image can be determined by a projection from the object tail. In
this case, I chose a ray parallel to the center passing through the far
focus.
dave.moore@tcbbs.cais.com
---
* Enter any 11-digit prime number to continue
* CMPQwk 1.42-17 1347
From: billbeskimo.com (William Beaty)
Subject: Re: A misconception spread by
Date: Mon, 5 Dec 1994 20:11:03 GMT
DAVE MOORE (dave.moore@tcbbs.cais.com) wrote:
: WB> ______________ /\__ __ - |
: WB> /^\ / \ --__ __-- |
: WB> | | | --__ __-- |
: WB> | | | --__ |
: WB> | | | __-- --__ |
: WB> | ______________| |__-- --__ |
: WB> \ / \|/
: WB> \/
: WB> object lens screen
: It's difficult to separate the limitations of ascii art from the point
: that you're trying to make.
Yeah, it's a bit difficult to discuss diagrams via usenet! The point I
was trying to make is that its a bad idea to use the above diagram to
explain how cameras and eyes work. Yet this diagram has become a sort of
science-cliche', at least in gradeschool texts and works of popular science.
I agree that INDIVIDUALLY each ray in the diagram is correct. But that
doesn't mean the diagram correctly explains how a camera works.
: However if one assumes near parallel rays
: from an object arbitrarily far away, the object appears to be smaller
: than the lenses regardless of the size. The classic example is that of
: stars.
I have to disagree. Distant objects need not appear smaller than the
lens. The night sky, if taken as a single "object," is enormous. The
sun, while far enough away that the light from its individual points is
parallel, does not shed parallel light. An object can be a billion miles
away, and a billion miles across, and its light is not parallel.So in
a diagram explaining the camera, light entering the lens should be shown
coming in from a variety of angles. Darn, I wish I could draw this
easily!
: The question in this diagram is why the image appears where it
: does rather than left or right. What's missing are rays through the
: lens center and focus to make the image position obvious.
True. But the diagram also is teaching that the light from the object
is focussed to a point behind the lens, then expands again to create
an inverted image. This idea has become widespread enough that it
appears on the front cover of a photography textbook, in color and in
detail. Very twisted concept!
Another thing I should make clear: The above diagram appears as part of
an explanation of the operation of cameras and eyes, NOT in physics
texts where the ray construction for locating real image distance appears.
The two situations are quite different. For example, a camera is an
opaque box with a hole in the front, while in the ray diagram, the lens
diameter is ignored and assumed to be infinite, which hides the mechanism
behind effects like depth-of-field and the camera-obscura geometry found
in simple (non-zoom) camera lenses.
: WB>By the way, here is a more correct version.
: WB> ___--- |
: WB> /\ ___--- |
: WB> /|\ ---___ / \ ___--- |
: WB> | ---___ | | ___--- |
: WB> | ---_| |- |
: WB> | ___-| |_ |
: WB> | ___--- | | ---___ |
: WB> | __--- | | ---___ |
: WB> \ / ---___ |
: WB> \/ ---___\|/
: WB> object lens screen
: Your diagram suffers from the same problem. Try this one:
: /\
: / \
: | |
: | |
: | | ___
: /|\ ----- | | ___ |
: | \ ----- | | ___ |
: | \ ----- | | ___ |
: | \ ---- | | ___ |
: | \ focus -| | focus ___ |
: | .......\...........|....|___.......___................|... Center
: | \ | | --- ___ |
: | _______ _____\_______| |_____-- ----- |
: \ | | ----- |
: \ | | ----- |
: \ | | ---- |
: object | | ___________________________\|/___
: | |
: \ / real image
: \/
:
: lens
:
: In the above: a ray from the object head passes in a straight line
: through the center of the lens. Another ray from the object head passes
: through the near focus and comes out of the lens parallel to the center.
: The intersection of these two rays defines the image point. The size of
: the image can be determined by a projection from the object tail. In
: this case, I chose a ray parallel to the center passing through the far
: focus.
Bravo! Geez, I wonder if there is a mouse-based drawing program for
unix that would let one draw directly in ascii art?
Your diagram is even more "correct," but I see that I didn't make my
original point clear. The intention of the diagram was to explain
cameras and eyes either to the general public, or to 5th grade students
(which is often assumed to mean the same thing.)
So, what is needed here is a diagram which answers these questions
in a simple obvious way:
HOW DOES A LENS TURN THE IMAGE UPSIDE DOWN?,
and
WHY DOES THE IMAGE PROJECTED ON THE FILM VARY IN BLURRYNESS AS
VARIOUS OBJECT/LENS/FILM DISTANCES ARE CHANGED?
That diagram at the top of this message answers these two questions
in a completely wrong manner. Yet that same diagram is used again
and again in numerous books which intend to explain eyes and cameras!
The diagram has become a Meme, living a life of its own in the
"culture dish" of the printed page.
.....................uuuu / oo \ uuuu........,.............................
William Beaty voice:206 bbs:206-789-0775 cserv:71241,3623
EE/Programmer/Science exhibit designer http://amasci.com/
Seattle, WA 98117 billbeskimo.com SCIENCE HOBBYIST web page
Date: 04 Dec 1994 16:05:07 GMT
From: Michael_Porter@carletonbe.ottawa.on.ca (Michael Porter)
Subject: Re: A misconception spread by texts
Newsgroups: k12.ed.science
William, the diagram that you criticise,
______________ /\__ __ - |
/^\ / \ --__ __-- |
| | | --__ __-- |
| | | --__ |
| | | __-- --__ |
| ______________| |__-- --__ |
\ / \|/
\/
object lens screen
...and the one you offer as "a more correct version",
___--- |
/\ ___--- |
/|\ ---___ / \ ___--- |
| ---___ | | ___--- |
| ---_| |- |
| ___-| |_ |
| ___--- | | ---___ |
| __--- | | ---___ |
\ / ---___ |
\/ ---___\|/
object lens screen
...are equally correct, and both misleading. Your diagram would suggest that
any lens to screen distance would provide a focussed image. Both diagrams
would be improved if an extra ray were added from each point on the object
(you could combine the two diagrams to achieve this). Where the rays cross
on the other side of the lens (_if_ they cross), you get a focussed, real
image corresponding to that point on the object.
Mike
