Talk:Lens (optics)/Archive 1

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Archive 1

Lensmaker's formula

Hello, just letting you guys know that the lensmaker's formula has a minus in there between the 1/R1 and 1/R2, not a plus. You can check other physics sources online for confirmation.

It depends on what sign convention one chooses for the curvatures. This is an arbitrary choice, and different sources choose differently.--Srleffler 11:19, 23 May 2006 (UTC)

how lenses are made

Hey folks, I must say this is the most understandable and concise page, that I know of, dealing with this subject matter. keep up the good work. Could you add a piece on how lenses are made? What equipment, processes, etc.? How large or small can they be made? How accurately can they be machined at such large and small dimensions? [User Randall Meyer]06 12 06

Split page

Would it not be an idea to split this large article? The chapter on optical aberration would be a good candicate User:Egil

I considered splitting off the aberration section before, but that would really require merging it with the aberration in optical systems article. That article is very dense and hard to read (being copied from the 1911 EB), so it'd be a lot of work.
As it stands, I don't think the current article is too long, and the aberration section is limited in scope to a single lens, which makes it fine in my opinion. It's also only a qualitative description of aberration, I think a quantitative treatment should reside in a seperate article. -- DrBob 17:45 Jan 24, 2003 (UTC)

Fine with me. I've put a link from aberration to lens. Wrt. the to do items, I've left them as unterminated links. So if you later feel for putting them into the lens article, then it would just be a matter of deleting the links. User:Egil


Who feel to write something about photographic lenses ?

PS: How do you add your name and the date to your answers? I assume it is automatic?

Argh, someone moving the article to lens (optics) means everything that links to the primary meaning of lens now goes through a redirect. Can someone move it back? I can't, because lens has a history and I'm not a sysop. -- DrBob 17:08, 5 Mar 2004 (UTC)

Oops - I am the guilty party - and I;m sorry. But I do think there is a good case for not treating the optical-instrument type of lens as the primary meaning. Willing to fix all the links manually - but only if there is agreement on how best to do it. Sorry for causing mess and hassle, but maybe it is time to make a change. -- Hugh2414 22:31, 7 Mar 2004 (UTC)

To me lens (optics) seems just fine. Lens has to many meanings for the previous arrangement. The primary lens page should be the disambiguation page though, i.e. no need for lens (disambiguation) IMHO. -- Egil 23:27, 7 Mar 2004 (UTC)
PS: But all the links must be fixed, there are now a number of double redirects! I assume the person doing the rename will also fix the links!

I have copied the contents of lens (disambiguation) into lens. Next step would be to fix all the links to lens to point (most of) them at lens (optics), and then get lens (disambiguation) deleted. I'll happily go ahead on a link-fixing spree. Just waiting to hear from DrBob -- Hugh2414 09:28, 8 Mar 2004 (UTC)

Sure, I'm probably biased towards the optical meaning, so leave the page at lens (optics) since that seems to be the consensus. You can use the "what links here" page to see which links need to be updated. Thanks. -- DrBob 15:53, 8 Mar 2004 (UTC)

Should one include Cartesian sign conventions in the part after the thin lens fourmula -- which states that when the distance of the image from the optical centre should be taken as positive and when the same should be taken as negative? -- Guest

I think, after checking, that the lensmaker's equation when d is small is 1/f=(n-1)(1/R1+1/R2) the change: plus instead of minus between the radiuses

^ No, I'm sorry, I think you are wrong about that. The lensmaker's eqn has to have a negative sign in it.

R sign in first paragraph

I think that it might be helpful to include the sign conventions for these lenses. If R1 is to the right of the lens, then it is positive, to the left of the lens then it is negative and so on. To include the conventions along with what is already there would be more informative.


This is really an excellent article, especially the diagrams. Kudos to those involved in constructing it. — brighterorange (talk) 17:58, 2 October 2005 (UTC)


Very nice article, but I wish it provdided proper citations for the early references to lenses. Actually, this is a common problem with Wikipedia: where articles often provide a link to Pliny, for example, (which anyone could type in a search box), when what would be useful would be specific citation for where in the Natural History (persumably?) he mentions a lens. --ThaddeusFrye 16:36, 21 November 2005 (UTC)

  • I've added a few links to cites from the history section that I can find. --Bob Mellish 18:44, 13 December 2005 (UTC)

eyeglasses aren't achromatic.

Anybody know why eyeglasses aren't made achromatic. I experience some difficulty because of this fact, and I would think that achromatic lenses would do away with much of the problems of Scotopic sensitivity syndrome Hackwrench 23:10, 29 December 2005 (UTC)

Achromatic lenses are necessarily much thicker than regular lenses. The result would be unsightly, and also much more expensive. There might also be problems with achieving good performance over a wide range of object distances. --Srleffler 19:08, 30 December 2005 (UTC)
Achromatic lenses are more thicker over the entire surface, but at their thickest points, shouldn't they be the same thickness? Hackwrench 23:09, 30 December 2005 (UTC)
Achromats are made by gluing together two glass lenses, made from glasses with different indexes of refraction and different Abbe numbers (a measure of dispersion). The pair are designed such that chromatic abberration in the two lenses partially cancels. Eyeglass lenses are pretty thin to begin with, so the achromatic combination would likely end up being thicker. Also, a certain thickness of each glass might be required to correctly cancel the aberration (I haven't done the calculations, so I can't say for sure.) Another issue would be that the optical power required for the first lens in the pair would be higher than your current lenses. The second lens reduces the optical power of the pair, so the first lens needs to be stronger to compensate.
There might also be material issues. Eyeglass lenses are usually made out of plastic these days. That might not be possible for an achromat. Also, the glass used for the second lens element in an achromat is less durable than standard optical glass.
Anyway, it might be possible, if you can live with these disadvantages. You must have an awfully strong prescription, though, if you actually see chromatic aberration from your eyeglasses. I have never heard of such a thing. --Srleffler 05:01, 31 December 2005 (UTC)

Differing Spellings

I feel it's most appropriate to use American English spellings in this article. A glancing review of the history of the field reveals that light and lenses are largely the domain of United States scientists. See Thomas Edison and Nicola Tesla. 03:23, 20 January 2006 (UTC)

You have misinterpreted the policy. If you need to review it, see Wikipedia:Manual_of_Style#National_varieties_of_English--Srleffler 04:42, 20 January 2006 (UTC)

I've always spelled it lense... its in my dictionary, but I guess that spellings uncommon. lists it as uncommon as well.

it should really be made clear that the difference is between American English and British English. The statement that only one dictionary uses it should definitely be changed as British dictionarys use Lense. -- (talk) 20:44, 22 December 2007 (UTC)

In order for that to be made clear, you'd have to show us the evidence. I'm unable to verify it. The first few books I could find with lense in them were American, and I haven't seen any Briish dictionary that says lense is the preferred spelling. What have you got? Dicklyon (talk) 21:16, 22 December 2007 (UTC)

My 1979 edition of the OED gives : "Lens" (pl. "Lenses") from Latin "Lens" meaning lentil (similar biconvex form) and the first usage it documents is 1693 by Edmond Halley (English Astronomer Royal), followed by Isaac Newton's Opticks (sic!) of 1704. The OED also gives : "Lense" (obsolete) as an Old English word meaning to make lean, to macerate; ie according to the OED "lense" is not a variant spelling of "lens", but an entirely different word. Curiously, "to make thin and/or pliable" seems like a more insightful analogy to the modern definition of a refractive lens than its resemblance to a lentil! (talk) 21:21, 17 August 2008 (UTC)

My 1991 Collins Dictionary (pub HarperCollins, Glasgow) has an entry for "lens" but nothing for "lense". (talk) 21:29, 17 August 2008 (UTC)

Can anybody produce a reference for a dictionary that uses the spelling "lense" to mean "lens"? I can't find any in the five large dictionaries I have, including Webster and OED. It seems to be a spelling that is becoming much more prevalent, and until proof of the contrary, I believe it is wrong. If nobody can come up with a reference, I propose to replace the word "obsolescent" with "incorrect". Groogle (talk) 05:20, 18 July 2009 (UTC)

You're probably right that it's basically just an error, though it appears in about 10 books per year for the last two centuries, it looks like. Some taught it pretty explicitly, like this one does. Some claim to be dictionaries of a sort, like this one. It's definitely more common, relatively, in older books. Your dictinaries probably aren't old enough to document the nineteenth century variant usage. Ah, but wait, here is a modern Merriam-Webster's with entry lens also lense. Maybe they made a mistake, too; or just took their job of documenting actual usage more seriously than some others. Dicklyon (talk) 07:01, 18 July 2009 (UTC)
Thanks for the research. Looking more carefully, the first two references mix "lens" and "lense" indiscriminately, so I suspect that's just carelessness. Merriam-Webster is obviously more important, but since their canonical dictionaries don't mention the spelling, I'd guess that this, too, is a misunderstanding. I've modified the article accordingly. Groogle (talk) 02:49, 19 July 2009 (UTC)
I reverted your changes for the moment. I'm open to changing the wording, but the new text must follow Wikipedia's policies on sourcing and original research. You're not permitted to analyze sources and draw your own conclusions, although simple observation of what sources say is permitted. You can say that major dictionaries do not list "lense" as an acceptable spelling. You should back that claim up with citations to the five major dictionaries you said you checked. You can't say that in the sources that do list it as acceptable, it "appears to be a typographical error used without explanation", because that is your own analysis of the sources, not a direct report of what the sources say. Your statement "No mainstream dictionary lists it as a correct spelling of the word." is problematic, because we do not have a source that says that, and I don't see any evidence that we have checked every mainstream dictionary. The citation that followed that statement actually contradicts what you wrote, saying that some dictionaries do list "lense" as acceptable.
The Merriam-Webster dictionary that lists "lense" as acceptable is an important counterexample, and we should include it as a reference in the revised text.--Srleffler (talk) 04:39, 19 July 2009 (UTC)

Gravitational lens

I am tempted to put gravetational lense as another subheading of optical lense. David R. Ingham 05:02, 20 January 2006 (UTC)

Gravitational lens has its own article.--Srleffler 12:36, 20 January 2006 (UTC)

Explanatory pictures

I like the article about lenses. However I have the feeling that the bending of the rays is not completely accurate. They are mostly bended at the central plane of the lenses which is a simplification as the rays bend as a result of changing optical properties i.e. at the interfaces air/lens or within the lens if the material properties of the lens change with location in the lens. It is especially important in the first picture as the refraction is neatly shown at both interfaces (going in and going out of the glass). However the rays within the lens are not paralel and this means that the crossing point of the rays is not the focal point of the lens but someway before the focal point. I think the definition of focal point is best illustrated with a plano-convex lens (incoming rays paralel to each other and axis of lens, crossing point of outcoming rays is true focal point).

20:34, 1 February 2006 (UTC)Dick Zijlstra 21:34 1 february 2006 (UTC)

  • It's fairly common to show the rays bending at the principal plane(s) of the lens rather than the surfaces, for thin lenses, though this isn't expained in the article. If someone writes an article on geometric ray tracing, this can be explained further. The 1st picture is correct - if the interior rays were parallel, this would correspond to the case of 2f - 2f 1:1 imaging, not imaging of a collimated beam to the focal point. --Bob Mellish 21:46, 1 February 2006 (UTC)
He has raised a good point, though. For an encyclopedia article like this one a diagram that shows the rays bending at the center of the lens is a bad diagram. The rays should bend where they actually bend.
There is already an article on ray tracing, although it is short on details and suffers from the overlap between optical simulation and computer graphics.--Srleffler 23:12, 1 February 2006 (UTC)
  • Fair enough. I have the Illustrator originals of the pics, so they're easy to tweak. --Bob Mellish 02:26, 2 February 2006 (UTC)
  • I've now uploaded new versions of the pictures with the rays bending physically. I've taken the opportunity to convert them the SVG format at the same time, so feel free re-size them as needed. --Bob Mellish 01:09, 6 March 2006 (UTC)

The rainbow is formed by water droplet due to dispersion and not by lens action (similar to a prism). Also, the picture of the rainbow does not appear to be real (it extends in front of the hills rather than falling behind them). Also the angle "appear" to be wrong (guessestimate). Best deleted.chami 05:09, 23 July 2010 (UTC) —Preceding unsigned comment added by Ck.mitra (talkcontribs)

(i) Ignore the colors, look at the shape of the rainbow. (ii) why should it go behind the hills? Yes, the picture is a bit odd, but I don't see a clear evidence it is fake. Materialscientist (talk) 05:22, 23 July 2010 (UTC)
I removed the image. It's not really suitable for this article. Raindrops form rainbows by a combination of reflection and refraction. It is misleading to describe them as "lenses". The image adds little to the reader's understanding of lenses.--Srleffler (talk) 16:48, 23 July 2010 (UTC)

thin lens formula / real lens formula

This page contains the thin lens formula. Is there a more accurate formula for non-thin lenses? Itd be nice to have it on this page. Fresheneesz 03:35, 4 March 2006 (UTC)

More than just a formula is required. Imaging with thick lenses is beyond the scope of this article. I just tonight created a (stub) article on the cardinal points, which is part of what is needed to understand thick lens imaging. I hope that eventually there will be an article on geometric optics that pulls all of this together and explains image formation in more detail.--Srleffler 04:07, 4 March 2006 (UTC)
Actually, it's not so bad. The formula for "thick lenses" is the same formula, but instead of measuring the distances from the center of the lens, you measure them from the principal planes of the lens (assuming the lens is in air).--Srleffler 01:38, 8 March 2006 (UTC)

Punctuation after equations

I propose removing the punctuation after equations, as equations are so extremely offset that a period or comma provides no extra readability to the sentence. Not to mention, a comma can be confused as a prime (especially confusing on pages about optics). Almost every page I've seen doesn't use punctation after equations, and having it here is simply an unnecessary annoyance. Comments? Fresheneesz 20:17, 5 March 2006 (UTC)

Requested move

Talk:LensLensLens (disambiguation) and Lens (optics)Lens: I realize that there are many major entries on Lens. But most of them relate to or derive from the optical meaning, and the optics use is still the primary use. Aside from the three places and the person, Laser Engineered Net Shaping and Lens (genus) are the only ones not falling under Lens (optics). I think it makes more sense to have the optical sense at Lens. Please discuss at Talk:Lens#Requested move. — Knowledge Seeker 05:44, 6 March 2006 (UTC)

Discuss at Talk:Lens#Requested move.

Perfect lens function?

The article says that, while being the most common lens shape, a spherical lens is not the optimal surface shape for a lens because it produces the so-called spherical aberration. However, the article fails to say what *is* the perfect surface shape for a lens. I mean, mathematically speaking (and forgetting things like chromatic aberrations), what is the surface function of the *perfect* lens which focuses light perfectly from all the surface of the lens? In fact, I cannot find this info anywhere for some strange reason. (My wild guess is that the perfect lens surface shape is a paraboloid, but I don't have any mathematical proof of this.)

The perfect shape depends on exactly what you're going to do with the lens, in particular how far away the object is and where you want the image to be formed. There is no one, single perfect shape. Perfectly or nearly-perfectly shaped lenses are available for particular applications. They are called aspheric lenses.
I'm not sure how paraboloids are for lenses, but I do know the answer for mirrors. Spherical mirrors exhibit spherical aberration as do spherical lenses. A parabolic mirror is the optimum shape for focusing light from a distant object (infinitely far away) to a point. An elliptical mirror is optimum for focusing light from one nearby point to another.--Srleffler 14:10, 19 May 2006 (UTC)

I second the original poster. This has to be common in optics texts. Or is the shape that produces no spherical aberration some nasty function of the index of refraction? —Ben FrantzDale 02:36, 4 November 2007 (UTC)

You seem not to have understood my answer. I'm not sure what more I can say that I haven't said above. --Srleffler 05:20, 4 November 2007 (UTC)
I think the answer Ben is looking for is "hyperbolic". According to Optics by Hecht, hyperbolic lenses will transform a spherical wave front into a planar wave front and so a convex hyperbolic lens will project a point onto another point. That doesn't say anything about chromatic aberration or distortion. The way the article is written now, though, would be analogous to the article about satellite dishes assuming all satellite dishes are spherical, glossing over the fact that that there is a "right" shape for them to be to focus exactly. 20:12, 8 November 2007 (UTC)


An anonymous editor changed a sign in the thin lens equation, but not the full lensmaker's equation. I was going to revert, but luckily I checked and found that (I think) the anon editor is right. The signs in these equations were not in accord with the sign convention explained on this page. They had originally been correct, but were flipped in this edit over a year ago. Nobody noticed. I fixed it and added a hidden comment to warn editors that different references use different sign conventions.

Could somebody please double-check that I haven't made a mistake.--Srleffler 14:13, 2 June 2006 (UTC)

Sign confusion

How can a distance possibly be negative? —Frungi 18:48, 2 November 2006 (UTC)

It's just a way of encoding direction in the same variable. You can have a distance in front of something or a distance behind it. By allowing the distance to have a sign, you allow a single variable to represent the position of one thing relative to another regardless of which side it is on, and you can construct formulas that work in either case. This idea of distance as relative position is analogous to displacement, as used in other areas of physics.--Srleffler 20:45, 2 November 2006 (UTC)
So which direction is negative? —Frungi 03:10, 3 November 2006 (UTC)
That depends on the sign convention one is using. Different books (etc.) use different conventions. The choice of sign convention determines the form that all the equations take. The choice is arbitrary, but once you choose you have to be consistent. This article appears to be using the convention that the object distance is positive if the object is in front of the lens, and the image distance is positive if the image is behind the lens (a real image). The other common choice would be to make both distances positive for things to the right of the lens, and negative for things to the left. If that choice is made, some of the signs in the equations have to be changed.--Srleffler 04:32, 3 November 2006 (UTC)

Lensmaker's equation again

In a recent edit someone fixed an error in the Lensmaker's equation. I was surprised that such an important equation could still contain an error after all this time. Even more surprisingly, I think I found another. The equation, as corrected, read:

I believe this should be:

The "incorrect" form seems to me to be a calculation of the distance from the front or rear focus to the corresponding principal plane, which is not the same as the focal length (or "effective" focal length) for a lens in a medium other than air or vacuum. I could have inserted my version, but that would be original research since I calculated it myself (and I don't want to insert a mistake if I am wrong). In the meantime, I have replaced the equation with one supported by citations—the form for a thick lens in air. I suggest that this be replaced with a more general formula only if the formula can be supported by a reference. It might be better to stick with the form for a lens in air to avoid confusion over the various focal lengths/distances exhibited by a thick lens in general media.

Focal lengths in general optical systems can get quite confusing. Consider the most general case: a thick lens with one medium on one side and a different medium on the other side. If neither medium has n=1, then the lens has five distinct focal distances:

  1. focal length or "effective" focal length (EFL)
  2. the distance from the front focus to the front principal plane
  3. the distance from the rear focus to the rear principal plane
  4. the distance from the front focus to the front vertex
  5. the distance from the rear focus to the rear vertex.

In general, these are all different. The terms used to describe them sometimes overlap, but the only one that can be called simply "focal length" is the first: EFL. Optics is a pain, once you move beyond the usual simplifications... --Srleffler 23:52, 13 December 2006 (UTC)

This formula:

does not reduce to the thin lens equation given in some textbooks (Hecht, as referenced by the article, gives it a step earlier in the derivation on page 158):

However, I agree that seeing there is no support in literature for it, the form you posted is probably best. -- 06:44, 15 December 2006 (UTC)

I don't see the equation you give in my second-edition copy of Hecht (which is the one referenced in this article). Perhaps I just missed it, or perhaps you are using a different edition. (If earlier, it might imply that this was an error that was corrected.) The ratio does appear in the section on refraction at spherical surfaces, but only because there Hecht is dealing with the front and rear ("object" and "image") focal lengths, not the true focal length. Hecht labels them and , not merely . I wouldn't be surprised if some authors have confused front and rear focal lengths with the focal length. If that is actually the case, it would certainly be a good argument for avoiding the issue here by not dealing with non-air media.--Srleffler 16:08, 15 December 2006 (UTC)

Sorry, I have the fourth edition. So if it was corrected mine would be the correct one. In my edition, equation 5.15 is the thin-lens equation and 5.14 is this:

If you solve for and take the limit as you get the equation I state above. This is fully supported by the proper derivation in the text.

Also, I haven't thought this through completely, but I don't think there is a case for thin lenses where you get front and rear focal lengths by simply changing the medium around it. -- 00:02, 16 December 2006 (UTC)

I see. You made a mistake. in media where . I don't have my texts handy, but I'm pretty sure the correct relation is:
Note that the distances from the thin lens to the foci are not , but rather . This ratio is known as the front (or rear) focal length, and is distinct from the actual focal length (one over the optical power of the lens).
If this seems not very sensible, it's because it isn't. It might have been better if optics was formulated from the beginning to use optical power () as the primary measure of a lens rather than focal length. Focal length is too easily confused with the distance from the lens to the foci, and the fact that we start by teaching the case of a thin lens in air, where these distances are equal, fosters this confusion. I strongly recommend Greivenkamp's little book, by the way (ref in article). It is very straightforward and made a lot of things clear that Hecht did not.--Srleffler 04:45, 16 December 2006 (UTC)

I suppose it is valid to define the equations that way but I have no textbook that does so. Mathematically, however they are equivalent. I've noticed that in optics, everybody and every textbook has a different set of conventions which are all valid providing you stick to them.

It appears that this article was written with the definitions that I use seeing all of the equations on the page have matched with what I said. Furthermore, I hadn't noticed this before but you have removed the definition of from the page and the thin lens equation still uses it. Something needs to be changed, which I will leave up to you. -- 21:51, 16 December 2006 (UTC)

I removed from the thin lens equation, restoring it to a form that is supported by a literature reference. The forms of both equations that included may have been "original research".
Yes, optics conventions differ between different references. I am not aware of a reference, however, that clearly defines focal length in such a way as to make the equations I removed from the page correct. If you know of a book that clearly defines focal length this way, please post a reference. While Hecht glosses over this issue, he is careful not to use or define focal length per se, until after he makes the assumption that the lens is in air. In particular, the equation appears only after this assumption has been made. He doesn't make clear that this equation in fact depends on that assumption, but it does.--Srleffler 20:11, 18 December 2006 (UTC)

(Note that this discussion is a good illustration of why Wikipedia's policy on original research is important, and why it applies just as much to physics as to other fields. Even though this seemed like a straightforward thing to derive from the equations in Hecht, it isn't.)--Srleffler 20:17, 18 December 2006 (UTC)


There seems to be a lot of sabotage in this article. After removing an out-of-place reference to testicles in the first paragraph, I noticed several more instances of similar things, such as "Recent excavations at the Penis harbor town of My Dick in a Box, Gotland in Sweden [...]" and "[...]probably in The Thong Song in the 1280s". Complete nonsens references to obscene things. If someone has the time to go through the history and revert to the real content, please do so! 19:07, 11 April 2007 (UTC)

It's vandalism [...]. 22:46, 13 October 2007 (UTC)
[Personal attack in above comment removed. Let's keep Wikipedia civil, please.--Srleffler 03:51, 14 October 2007 (UTC)]

Missing Lens Type?

Under Types of Lenses, the most common type of lens used to treat myopia is missing both from the text and the graphic. That would be the Concave-convex lens. Just look at the assymetry in the chart. Meniscus should be in exact center. To the left is Convex-concave, so Concave-convex should be to the right, but it is missing. As a nearsighted person, my glasses are concave-convex, ie., they are more concave than they are convex. They are thicker on the outside and thinner in the middle (smaller curve on the inside). Convex-concave would be thicker in the middle and thinner on the edges (smaller curve on the outside). Meniscus (in the pure sense) would be equally thick all the way around.

Of course, my disagreement here could just be semantics. The lens formerly known as concave-convex (diverging) might just be lumped in with the convex-concave (converging) lens. So maybe concave-convex is now known as a diverging convex-concave lens.-- 09:33, 30 June 2007 (UTC)

The article doesn't distinguish based on which surface is on the inside. As defined there, "a lens with one convex and one concave side is convex-concave". --Srleffler 05:30, 4 November 2007 (UTC)

The term "meniscus lens" has been incorrectly applied to concave-convex optics that have the same curvature on both surfaces, a form that is more appropriately called simply a "dome" and does not form any optical image. The first to use the term "meniscus lense" was Stephen Gray in the 17th century (see Philosophical Transactions, volume 4, 1694-1702, pp. 97-101) in conjunction with his writings on optical experiments using water droplets held in place by surface tension within metal rings. The curvature of the water droplet lens is then a function of water's surface tension in air, the attraction of the water molecules to the supporting ring, and the size of the water droplet and ring. A water droplet held in place solely by a metal ring, as described first by Gray, produced a concave-convex convergent lens that could be used as a simple microscope. In the early 19th century it was found that the true meniscus lens provided less distortion than did a convex-convex magnifying lens when used in the camera obscura of the day. Reduction of distortion in the camera obscura was important since in those days this device was generally used for making drawings, particularly drawings of architecture where distortion was a problem when using a convex-convex lens to form an image. In common use the term reasonably can be extended to describe a divergent lens where the concave surface curvature is greater than that of the convex surface though such a lens would likely be part of a multiple element lens since in its simple form it will not form an image. If one uses the term to describe symmetrical convex-concave optics, it should be done so with the understanding that such optics are not strictly a lens as the term has been defined.—Preceding unsigned comment added by L. David Tomei (talkcontribs) 08:07, December 19, 2007

Thanks for this message. This is great information. It would be good to get it into the 'pedia somewhere. I'm not sure where the best spot would be though. Just to be pedantic, a lens with the same curvature on both surfaces does actually have some optical power. In air, the optical power is
where is the index of refraction of the lens, is the curvature of the surfaces (=), and is the thickness of the lens. So, a 1 mm thick crown glass meniscus lens with both surfaces having 100 mm radius of curvature has a focal length of about 25 m. One can make an optical element with no optical power. The correct curvatures for this are close to equal, and can be easily calculated from the thick lens formula. --Srleffler (talk) 18:55, 19 December 2007 (UTC)

Note on top

I believe we don't need the note

at the top of the article. This article is about lenses in optics. There is nothing ambiguous about that. If you put a note here pointing back to lens you need to do the same thing at Lens (anatomy), Corrective lens, gravitational lens, and all the other meanings. I don't think this is the way disambiguation pages are supposed to work. Comments? Oleg Alexandrov (talk) 05:47, 4 February 2008 (UTC)

Agreed. I removed it. The only argument I can see for that otheruses is if there are redirects to this page.—Ben FrantzDale (talk) 12:44, 4 February 2008 (UTC)
I had opposed this, but after reviewing WP:disambiguation and WP:HAT, I stand corrected.--Srleffler (talk) 17:21, 4 February 2008 (UTC)
Second thoughts: It seems to me that "Lens (optics)" is, in fact, ambiguous. It is ambiguous with Lens (anatomy), Corrective lens, and Photographic lens, all of which are optical lenses.--Srleffler (talk) 03:40, 23 April 2009 (UTC)

Types of lenses

I undid some changes made by other editors in the structure of the section on lens types. Edits by several people had resulted in concepts and terms being used before they were defined. The flow of the section now is to first introduce the various lens shapes, with a drawing showing all of them. Then it defines what it means for a lens to be "positive" or "negative", in the context of the lens types which by their nature fall into one category or the other. Finally, it deals with the more complicated case of meniscus lenses, which can be either positive or negative. The term optical power is now linked to the relevant article. --Srleffler (talk) 03:49, 22 February 2008 (UTC)

Rifle scopes

Hi, first I would like to thank all the contributors for this page as well as the related ones, these are a great resource they are EXCELLENT. Lenses play a big role in military and hunting scopes. Perhaps there could be a section on one of the pages about this. I am looking for info on things like eye relief, parallax, and magnification. Basically looking for "how it works" Thanks, MattTheMan (talk) 01:20, 30 April 2008 (UTC)

The right place for info specific to rifle scopes would be at Telescopic sight. For more general info, try Eye relief, Parallax, and Magnification.--Srleffler (talk) 01:37, 30 April 2008 (UTC)
Thanks! What a speedy response haha. I went to the talk page of the red dot sight article. MattTheMan (talk) 04:35, 30 April 2008 (UTC)

Plastic lense details-- how manufactur —Preceding unsigned comment added by (talk) 13:24, 29 May 2008 (UTC)

Refraction through Lens(Biconcave and Biconvex).

I have studied that the light rays coming directly straight and parallel to each other at the biconvex or biconcave lens doesn't refract at the first concave or convex lens(i.e., before the aperture). But after they strike the aperture of lens, they get deviated from their original path(i.e., they get refracted) and later converge in case of convex lens and diverge in case of concave lens. Moreover, the light ray which strikes the lens right in the middle part passes on undeviated through the principal axis. Now, my questions are:

  1. Why don't the light rays get refracted while striking the lens initially at the first lens?
  2. Why does the light ray that strikes the lens at the middle passes on undeviated through the principal axis. —Preceding unsigned comment added by Afnan01 (talkcontribs) 16:07, 16 July 2008 (UTC)
I don't follow your initial statement. Light doesn't bend at the aperture (except for the unusual case that there is a lens there). In response to your two questions: (1) Light does get refracted when it gets to the first lens surface with the exception of the ray traveling along the optical axis. (Actually, all rays entering the first surface normal to the first surface enter the glass without bending, but all but the the ray on the optical axis will bend when they leave the first element because they won't also be traveling normal to that interface. (2) That ray doesn't refract because it is traveling normal to the surface, so it's locally like shining a laser directly through a pane of glass: it just goes strait through. —Ben FrantzDale (talk) 02:14, 17 July 2008 (UTC)
I agree with Ben. Afnan, you appear to have been taught incorrectly. With ordinary optical materials such as glass, the light rays bend only at the surfaces of the lens. What might have you confused is the simple construction normally used for ray tracing by hand. One typically draws rays between object and image points using a few simple rules, such as "rays parallel to the optic axis are redirected to pass through the focal point on the other side of the lens". The ray paths one gets this way are approximate. They assume the lens is thin, i.e. of negligible thickness. For this reason, the rays are often drawn as bending at the center of the lens rather than at its surfaces. The approximation is not bad for a real lens that isn't too thick. If you trace the rays with them bending at the center of the lens, the part of the ray paths that lies outside the lens is fairly accurate. If you erase the portion of the line that lies inside the lens and draw a new line that connects the points where the path crosses the lens surfaces, you get a decent approximation of the true path of the ray inside the lens.
In this simple approximation, rays that pass through the center of the lens are treated as undeviated. This would be true for a hypothetical infinitely-thin lens, but is not actually true for a real lens. --Srleffler (talk) 05:31, 17 July 2008 (UTC)

Alhazen and eyeglasses?

(the Book of Optics) translation into Latin in the 12th century was instrumental to the invention of eyeglasses in 13th century Italy. [Kriss, Timothy C.; Kriss, Vesna Martich (April 1998), "History of the Operating Microscope: From Magnifying Glass to Microneurosurgery", Neurosurgery, 42 (4): 899–907, doi:10.1097/00006123-199804000-00116 ]

I have rm'ed the above claim to talk for clarification. There are actually many citations on the history of eyeglasses that state optical theory of that era had nothing to do with their development. There was a miss-concept how images were thought to be refracted on the back surface of the eyes lens, so eyeglasses would have no effect, vision problem were thought to come from an overall "diseased eye". Vincent Ilardi in Renaissance Vision from Spectacles to Telescopes states "Optical theory had nothing to do with the invention (of spectacles)[1]" and elaborates on page 28 how "writings" from "learned circles" from Alhazen down were so incorrect on their theories of vision as to be totally useless to opticians. Need rectify this citation versus the "History of the Operating Microscope" citation as to the claim "was instrumental to the invention". Fountains of Bryn Mawr (talk) 17:51, 9 December 2008 (UTC)

I have restored it and invited you to add other points of view, also sourced. There's no reason to remove info thats based on a cited reliable source just because you know of other sources that disagree; work on improving it, not destroying it. Dicklyon (talk) 22:51, 9 December 2008 (UTC)
I notice that the article here also claims that Alhazen's book "described how the lens in the human eye formed an image on the retina", which seems to conflict with what the Ilardi reference says.--Srleffler (talk) 04:33, 10 December 2008 (UTC)
I removed the statement and reworked the text. Book of Optics has cited statements that also contradict this uncited claim.--Srleffler (talk) 04:48, 10 December 2008 (UTC)

Chromatic aberration

The article needs to clearly distinguish between lateral and axial chromatic aberration. Neither this article nor Chromatic aberration does so. --Nantonos (talk) 09:04, 20 October 2009 (UTC)

Inappropriate picture

It is not appropriate to have the picture wiki/File:GGB_reflection_in_raindrops.jpg in an article about lenses: it is a picture of reflection, not refraction. Fathead99 (talk) 17:31, 22 December 2009 (UTC)

Disagree. That picture shows refraction and lensing effect by water droplets. No reflection whatsoever. Materialscientist (talk) 02:26, 23 December 2009 (UTC)

OK, well can the name of the file be changed then, eg to wiki/File:GGB_refraction_in_raindrops.jpg or something like that? Fathead99 (talk) 15:06, 23 December 2009 (UTC)

Yes it's a bad filename; ignore that, as it's hard to change. Dicklyon (talk) 16:47, 23 December 2009 (UTC)
I agree with MatSci and Dick: the image is clearly misnamed; it shows refraction not reflection. As Dick says, just ignore the filename. Images cannot be easily renamed.--Srleffler (talk) 23:25, 31 December 2009 (UTC)

This picture is shown upside down, giving the impression of holes in the substrate. Rotate your screen (or your head!) through 180 degrees and you will see the proper impression of water droplets. (talk) 21:00, 27 March 2010 (UTC)PI

Lensmaker's equation

The focal length of a lens in air can be calculated from the lensmaker's equation:[1]

Equation shows the power of the lens in dioptre.

To calculate directly to the lens focal length is used the following equation (if the lens is surrounded by air n1 = n3):

f '= n . R1 . R2 / (n-1) [n . (R2 - R1) + (n-1) . e]

An example: [2] --Tamasflex (talk) 17:53, 20 March 2010 (UTC)

The form you propose is undefined when one of the surfaces is flat (R1 or R2=∞), which is a very common case in practice (plano-convex and plano-concave lenses). The equation can of course be solved by rearranging to the 1/f form, or by taking the limit as R1 or R2 goes to infinity and applying L'Hôpital's rule. Calculating 1/f instead is much simpler. The 1/f form is also clearer physically: the optical power of the lens gets a contribution from each surface that is proportional to that surface's curvature, and in addition there is a contribution that depends on the thickness of the lens (vanishing in the thin lens limit.)--Srleffler (talk) 18:22, 20 March 2010 (UTC)

Why accomplices: For planconvex lens (positive or negative): f '= r / n-1 Diameter of center does not affect focal length. To calculate a complete lens (f, D, d, z, z ', s, s', p and other) problem is a little difficult but you have to use L'Hôpital's rule. And you said something.[3] --Tamasflex (talk) 19:29, 20 March 2010 (UTC)


Ilardi, Vincent (2007). Renaissance vision from spectacles to telescopes. American Philosophical Society. ISBN 9780871692597. Retrieved 20 July 2010.  this would make a great source for the article. Its got a lot from really early stuff in chapter 1 pg 35 J8079s (talk) 05:35, 20 July 2010 (UTC)

  1. ^ Greivenkamp, p.14; Hecht §6.1