Newsgroups: k12.ed.science 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. > > > > ___--- | > > /\ ___--- | > > /|\ ---___ / \ ___--- | > > | ---___ | | ___--- | > > | ---_| |- | > > | ___-| |_ | > > | ___--- | | ---___ | > > | __--- | | ---___ | > > \ / ---___ | > > \/ ---___\|/ > > > > object lens screen > > > Hmm, not exactly "more correct", you simply picked a different > pair of light rays to follow. Oooops! I should have called it "less misleading." > > 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. > 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