Talk:Lens (optics)
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[edit] 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)
[edit] 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
[edit] 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
[edit] unheadered
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.
[edit] 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.
[edit] Praise
This is really an excellent article, especially the diagrams. Kudos to those involved in constructing it. — brighterorange (talk) 17:58, 2 October 2005 (UTC)
[edit] Citations
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)
[edit] 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)
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- 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.
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- 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.
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- 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)
[edit] 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. 128.12.16.233 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. http://www.wsu.edu/~brians/errors/lense.html 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. --86.31.39.161 (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)
[edit] 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)
[edit] 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)
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- 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.
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- 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)
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- Fair enough. I have the Illustrator originals of the pics, so they're easy to tweak. --Bob Mellish 02:26, 2 February 2006 (UTC)
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- 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)
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[edit] 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)
[edit] 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)
[edit] Requested move
Talk:Lens – Lens → Lens (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 দ 05:44, 6 March 2006 (UTC)
Discuss at Talk:Lens#Requested move.
[edit] 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)
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- 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. 155.212.242.34 20:12, 8 November 2007 (UTC)
[edit] Signs
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)
[edit] 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)
- So which direction is negative? —Frungi 03:10, 3 November 2006 (UTC)
[edit] 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:
- focal length or "effective" focal length (EFL)
- the distance from the front focus to the front principal plane
- the distance from the rear focus to the rear principal plane
- the distance from the front focus to the front vertex
- 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. --68.148.27.42 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 (n − nm) / n 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 fo and fi, not merely f. 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. --68.148.27.42 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 f, but rather f / nm. 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 nm from the page and the thin lens equation still uses it. Something needs to be changed, which I will leave up to you. --68.148.27.42 21:51, 16 December 2006 (UTC)
- I removed nm from the thin lens equation, restoring it to a form that is supported by a literature reference. The forms of both equations that included nm 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)
[edit] Sabotage...
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! 84.217.137.13 19:07, 11 April 2007 (UTC)
- It's vandalism [...]. 201.29.183.92 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)]
[edit] 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.--65.190.103.147 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 (talk • contribs) 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
- φ = (n − 1)2C2t,
- where n is the index of refraction of the lens, C is the curvature of the surfaces (=1 / R), and t 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)
[edit] Note on top
I believe we don't need the note
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For other uses, see lens.
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)
[edit] 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)
[edit] 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)
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- 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 59.94.133.196 (talk) 13:24, 29 May 2008 (UTC)