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Old questions[edit]

Question: What correlation does the dioptre have with a person's 20/x vision? Is there a one-to-one correlation, and if so is there a conversion chart?—The preceding unsigned comment was added by Dimmer (talkcontribs) 18:43, August 25, 2005.

They are probably correlated, but not one-to-one. The "20/x" is a measure of visual acuity, which depends on the amount of refractive error (measured in dioptres), but also on other things. If you have a cataract, for example, your visual acuity will be poor, even though you may not need any dioptric correction at all.--Srleffler 05:21, 20 February 2007 (UTC)
Here is an unsourced chart:
Dioptres 20/something
-0.5 20/25 to 20/30
-1.0 20/30 to 20/50
-3.0 20/300
-4.0 20/400
-5.0 20/600
Dioptres 20/something
+0.5 20/25
+1.0 20/40
+2.0 20/70
+3.0 20/100
+4.0 20/200
I understand this doesn't account for cylindrical (astigmatism), cataracts, or other problems, but a rough guide like this is very useful. -kslays 17:39, 19 June 2007 (UTC)

Request for additional info: Diopter is also the name of a series of lenses used to increase the magnification of camera lenses in macro photography. This is the info I was looking for when I sought out this article. For instance, see this article at—The preceding unsigned comment was added by (Talk) (talkcontribs) 08:19, October 24, 2005.

Sounds like somebody just misunderstood. These add-on lenses increase the optical power of the camera lens. That is, they "add dioptres" to the focal power of the lens. It's not the name of a series of lenses; it's just a description of their purpose.--Srleffler 05:21, 20 February 2007 (UTC)
Actually, they are using an older meaning of the word. While the modern meaning is a unit of measure for lens focal length, the word diopter used to refer to:
  • Any lens system (such as a telescope)
  • A theodolite or similar surveyor's angle measuring device
  • An alidade
  • A surgical speculum
  • An instrument for drawing the skull by projections.
Diopter in the modern sense only dates to 1872, while the general word derives from Latin (dioptra) or Greek (διοπτρον) - a spyglass.
Arthur Koestler states (The Sleepwalkers) that the modern use was derived from the title of Johannes Kepler's book on optics. However, I can't find a source that specifically states that (Frederick or Felix?) Monoyer stated so in his 1872 article in Annales d'oculistiques. There is no online copy of the article and I have no access to a good French medical school library.
--Michael Daly 19:02, 21 October 2007 (UTC)

Optical power[edit]

I changed the link for "optical power" back to focal length, because the page refraction does not explain this term at all, while the page on focal length does. Optical power is simply a measure of focal length, nothing more or less. (It is, of course, one over the focal length.) Refraction, on the other hand, is one physical process that can produce an optic with optical power. (Reflection being another such process.)--Srleffler 06:18, 2 December 2005 (UTC)

I understand your point, but something needs to change. The introductory sentence has two links to focal length in it, thus the sentence reads: "A dioptre, or diopter, is a unit of measurement of the [focal length] of a lens or curved mirror which is equal to the reciprocal of the focal length measured in metres (i.e. 1/metres)." It's a circular definition. Edwardian 07:21, 2 December 2005 (UTC)
What's wrong with having two links to focal length in a sentence? The sentence uses two words that are best explained by that page. A link is not necessarily a synonym. Optical power is the reciprocal of the focal length. The focal length page covers two concepts: focal length and its reciprocal.
The problem is that it makes the definition appear circular. I think there needs to be an article entitled "Optical power" that we can link to because it is not "simply a measure of focal length". Help me with this analogy:
Force is an external cause responsible for any change of a physical system.
Force equals mass times acceleration.
The newton is the unit of force.
Optical power is one over the focal length (Srleffler 06:17, 3 December 2005 (UTC))
Optical power equals one divided by focal length.
The diopter is the unit of optical power.
-Edwardian 15:44, 2 December 2005 (UTC)
As I filled in above, optical power is really not an independent physical quantity. Unlike force and mass, optical power and focal length are not two different physical quantities. They are two measures of the same thing. Optical power is just a convenient mathematical shorthand for focal length. It is convenient because for thin lenses the focal length of the whole lens is approximately equal to the inverse of the sum of the inverses of the focal lengths each surface would have on its own. Because of this relationship, it is convenient to characterize surfaces and lenses by one over their focal length. "Optical power" is just the name given to this convenient representation of focal length. It has no other significance, and isn't really used much in optics outside of opthalmology. Calculations of lens combinations using optical power are not accurate. Adding powers only gives an approximation to the correct answer. --Srleffler 06:17, 3 December 2005 (UTC)
Regarding "[Optical power and focal length] are two measures of the same thing.": What do you consider "the same thing" to be? (BTW, the significance to ophthalmology is precisely what I have in mind here.) Edwardian 07:09, 3 December 2005 (UTC)
When an optometrist or opthalmologist puts a lens of a given optical power in front of a patient's eye, what he or she is doing is adjusting the focal length of the patient's visual system. A patient with myopia has an eye lens whose focal length is too short. A patient with hyperopia has a lens whose focal length is too long when at rest. I presume that for the case of the eye+external lens system, the inverse of the combined system focal length is approximately equal to the sum of the inverses of the eye and external lens focal lengths, since otherwise "optical power" would not be very useful. Note that this relationship is not true in general: the optical power of an optical system is not always equal or even close to the sum of the optical powers of the elements. For example, one can make a simple telescope with two lenses, each with positive optical power, but with a combined optical power of zero. The system is afocal. These are very often used as laser beam expanders, since a collimated input beam produces a collimated (but larger) output beam.--Srleffler 08:24, 3 December 2005 (UTC)
It appears that I’ve done a poor job making my point clear; that is, that “optical power” needs an article that includes a definition of the term.
Optical power and focal length are not two different physical quantities, but they are indeed conceptually different… otherwise two different terms probably would not exist. The optical power for a specific lens is measured as “one over the focal length”, however, that is not the definition for the general concept of “optical power”. If “one over the focal length” is the definition of optical power, then the first sentence above becomes: “When an optometrist or opthalmologist puts a lens of a given [one over the focal length] in front of a patient's eye, what he or she is doing is adjusting the focal length of the patient's visual system.” Conceptually it doesn’t make much sense.
Someone who works day-in and day-out with different optical systems can probably mentally switch from one abstraction or concept to the next so easily that its second nature for them. To make it easier for everyone else, would you object to something like the following?
Optical power is the degree to which a lens or mirror converges or diverges light. It is measured as the inverse of focal length. The dioptre is the unit of measurement of optical power.
Cheers! - Edwardian 06:26, 5 December 2005 (UTC)
This looks reasonable to me, although it's not clear that this can ever really be more than a dictionary definition, which was why I didn't think there should be an article on optical power. If you think there is enough to say to merit an article, go for it.--Srleffler 17:34, 5 December 2005 (UTC)
FYI, I created Optical power and edited the first line of this article to link to it. I may not do it immediately, but I do think there is more to add to it. Thanks again. Edwardian 19:43, 5 December 2005 (UTC)
  • I kind of favour separating articles like this, so I say go ahead. --Bob Mellish 17:55, 5 December 2005 (UTC)

Article Improvement Drive[edit]

Contact lens is currently nominated to be improved on Wikipedia:Article Improvement Drive. Please support the article with your vote. --Fenice 10:51, 16 January 2006 (UTC)


The diopter is stated to be a non-SI unit of measurement. Is there an SI equivalent? 19:28, 17 July 2006 (UTC)

The SI unit for optical power is inverse meters (m-1).--Srleffler 22:43, 17 July 2006 (UTC)

Magnification and dioptres[edit]

I removed the section on converting between magnification and dioptres. It had several serious flaws:

  1. This "conversion" is particular to magnifying glasses and other simple magnifiers. It is not a general property. The material is better placed in the article on magnifying glasses (I will add it there). It is in fact already covered at magnification, although in different terms.
  2. The section (and the reference from which it is drawn) makes an incorrect distinction between magnifying power and "total power".
  3. The definitions given are incorrect.
  4. The section confuses the physical quantity (optical power) with the unit of measure of that quantity (dioptres).

The magnification of a magnifying glass is a bit complicated. As can easily be verified by playing with one, the actual magnification ("magnifying power" or "angular magnification") of a magnifying glass depends on where you put it, and where the object is. The maximum magnification possible is obtained by putting the lens very close to your eye and moving your eye and the lens together to obtain the best focus. The object will then be typically also close to the lens. The magnifying power obtained in this condition is ¼Φ+1, where Φ is the optical power in dioptres. This is the value used for the "m×" measures of magnification. It is the maximum magnifying power obtainable with the magnifier.

Magnifiers are not always used this way, however. It is much more comfortable to put the magifier close to the object (one focal length away). The eye can then be a comfortable distance away, and a good image can be obtained very easily; it isn't very sensitive to the eye's exact position. The magnifying power in this case is roughly ¼Φ.

Interestingly, the magifying power also depends on how old you are. The factor of ¼ assumes a "standard" eye, typical of an adult. A young child obtains much less benefit from using a magnifier, because the child can obtain just as good an image by moving the object closer to her eye. The actual magnifying power experienced by the child with a lens is less.

Reference: Hecht, Eugene (1987). Optics (2nd ed.). Addison Wesley. pp. 186–188. ISBN 0-201-11609-X.  --Srleffler 05:49, 28 November 2006 (UTC)

thank you! Openlander 19:28, 28 November 2006 (UTC)

Night vision and dioptre[edit]

I've heard dioptre measurements used in the context of Night vision - does anyone know how such measurements would be calculated? ··gracefool | 02:07, 20 February 2007 (UTC)

Dioptres are a measure of magnifying power. As far as I can see, they have no connection to night vision at all, except that a night vision system might also magnify the image.--Srleffler 04:14, 20 February 2007 (UTC)
I often see "diopter" used with night vision devices where people are specifying the focus range of the night vision device's eyepiece (-4 to +2 Diopters, for example). One can usually focus this eyepiece so that eyeglasses are not necessary when using a night vision device. This makes them more comfortable to use, but the user must remember to remove and replace their glasses when switching between using the NVGs and not.WikimikeCA (talk) 18:05, 26 September 2008 (UTC)

Section on measuring dioptres deleted[edit]

I removed some recent additions [1] since it was more of a how-to guide, rather than WP style, and all the text was embedded as a diagram (and thus not editable). It could possibly be useful as an article on lens clocks, if re-written in a conventional style. --Bob Mellish 06:09, 29 June 2007 (UTC)

Examples of how dioptric power can be measured from curvature[edit]

Conventional text doesn't offer the fonts necessary to write the mathematical equivalents necessary to describe how curvature can be used in a lens of known refractive index to give a mechanical measurement of diopters. The necessity of .jpg files to do this seemed to be the easiest solution. Although this approach is all or nothing, still it gives a valuable demonstration on the visual learning gleaned from how a lens clock measures dioptric power. StationNT5Bmedia 16:25, 1 July 2007 (UTC)

I missed this earlier, but in case you're still around: Wikipedia has full LaTeX math markup. See Help:Displaying a formula for information on how to format math.--Srleffler (talk) 15:17, 27 September 2008 (UTC)


I added an etymology section to show that the term was originated by Kepler. This was removed and replaced with a comment that it was earlier used by Kepler. Coining a term and using a term are not the same thing. If someone can find an earlier source for the term and therefore show that Kepler was just using an accepted word then this latest edit should stand. Otherwise, I think that a section that points to Kepler as the originator is better. (talk) 19:49, 3 March 2013 (UTC)

I moved it back into the footnote and added the comment about Kepler "using" the term, because of a few different concerns. Your "etymology" section contained only the claim that Kepler coined the term, without the statement already in the article that the usage discussed here was proposed by French ophthalmologist Ferdinand Monoyer in 1872. I could have addressed this problem by including that information in the etymology section, but in this case I felt it was better to keep the discussion of origins of the term all together in the lede, and keep it brief. (Normally I dislike having any discussion of etymology in the lede of an article, but in this case it seemed appropriate.)
I find the claim that Kepler "coined" the term dioptre, as used here, to be dubious. I suspect that that statement comes from some editor mis-describing Kepler's book title Dioptrice as a first use of the modern term dioptre (or diopter). This is mistaken. The person who "coined" the term is the first one to have used the modern word with its modern meaning. I highly doubt that Kepler did so, but I didn't want to remove the claim altogether so I settled for moving it back into the footnote. I will now remove it altogether. If Kepler actually used "dioptre" to refer to inverse meters, you can add it back in. A specific reference would be helpful.--Srleffler (talk) 22:11, 3 March 2013 (UTC)

Approximate distance between "lens system" and retina.[edit]

The article said (about) 2/3 of total power of eye was from cornea and (about) 1/3 was from the lens. This is a total of 3/3 or 1.0. Srleffler suggested in an edit comment that the vitreous would have an effect on the actual distance from the lens system to the retina, so that it wouldn't actually be 1/(total power). Yet, the text suggests that all (2/3 + 1/3) of the approximately 60-d refractive power of the eye comes (only) from the lens combined with the cornea (the "lens system"). That suggests to me that the contribution of the vitreous must be is small, at least small enough to be unimportant to the article's purpose of explaining "diopter". And so, it would be reasonable to ignore it when asserting that the distance is "about" the same as the 1/60 meter figure obtained by the simple conversion of power to focal length.

I would also say that the "1/60" figure, which is self-evidently the result of the simple definition of "diopter" given in this very article, is not WP:OR. If it was, we would have to have to find some secondary source somewhere that said specifically that "60 Diopters corresponds to a focal length of 1/60 meter", and that would be silly. I'm not sure though if Srleffler was calling "1/60 m <-> 60 d" WP:OR or something else.

The thickness of the lens system (lens plus cornea) is obviously large compared to focal length for the eye. So, any distance to it would be approximate unless the "center" of the system were defined. However, this article's topic is "diopter" rather than "precise description of the human eye", so it's probably a distraction to get wrapped up in that level of detail. The main reason we're talking about human eye is to give some compelling examples to assist in explaining "diopter". The paragraph already used "approximately" and "about" to suggest the level of precision appropriate here. I continued that use that to appropriately "gloss over" the details unimportant to effective examples for "diopter". (talk) 03:02, 20 October 2014 (UTC)

Hi. The error you're making is that you are confusing focal length with "distance from the lens to the image plane". These are not the same thing. There are at least three problems with confusing these two distinct concepts. One is that, as you know, they can only be strictly equal for a thin lens. For a thick lens, the required analysis is more complicated, and involves the principal planes of the lens (not the "center"). The second problem is that even for a thin lens the focal length is only equal to the image plane distance when the lens is focused on an object at infinity. As you sit at your computer reading this, you can be sure that your eye is imaging the text onto your retina, which certainly would not happen if the distance from your eye's lens to the retina were equal to the focal length—even if the lens were thin.
The worst of the three problems with confusing focal length and image plane distance, though, is that even for a thin lens focused at infinity they are only equal if that thin lens is in air. If the lens has air on one side and water or gel on the other (as in the eye), the distance from the lens to the image plane is nf, where n is the index of the medium, and f is the focal length. For a normal eye, that means that when the eye is relaxed the retina should be about 2.2 cm from the rear principal plane of the lens. Obviously, this is WP:OR and not suitable for the article, but note that the outside diameter of an adult human eyeball is about 2.4 cm.
This is a good example of why we have our policy on No original research and of requiring citations. Sometimes even things that seem obvious are not.
I recommend not trying to work focal length into the section on the eye. Focal length is easy and intuitive for simple problems involving thin lenses in air, and becomes progressively less so as one moves away from that case. You're not going to find a truthful way to incorporate focal length into the discussion of the eye that helps a naive reader to understand dioptres better.--Srleffler (talk) 04:45, 20 October 2014 (UTC)

Please don't try to lecture on OR policy. I understand OR thoroughly. You're also assuming things I didn't write, please try to be more careful. My argument is/was that a certain amount of glossing over those very good points you make (thick lens, etc.) is acceptable in greater service of giving examples of the topic at hand ("diopter"). If glossing-over (via "approx" and "about") isn't to your liking, then fix it by mentioning the things causing variations from thin-lens estimate and that the thin-lens estimate is still pretty good (which it is). Regarding the "OR" of adding that, given how informed you are on the subject, I imaging that you in particular could easily find sources for it right on your shelf. (talk) 06:02, 20 October 2014 (UTC)

Reread the paragraph above that starts with "The worst of the three problems..." This is not a small correction, it is not a "thin lens" issue, and it fundamentally contradicts what you are trying to do. You are trying to explain optical power by relating the focal length to the distance between the eye's lens and retina, but fundamentally the focal length is not related to that distance in the way you suppose. Claiming that the focal length is the distance between the lens and the retina is not just inaccurate—it is fundamentally wrong. --Srleffler (talk) 16:38, 20 October 2014 (UTC)

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Error? Human eye relaxed optical power[edit]

Section "In vision correction" currently says: "In humans, the total optical power of the relaxed eye is approximately 60 dioptres.[4]"

This does not seem to correspond with the reference given, nor with other references I have seen. Assuming "relaxed eye" means "minimum accommodation" (viewing infinite distance), most references give an optical power of 40 to 45 diopters. They then attribute to the crystalline lens an additional 15 to 20 diopters. Unless I am misunderstanding the current narrative, it appears to make one or other of these mistakes: suggesting that the relaxed eye incorporates the maximum power of the lens, or suggesting that the maximum optical power is 60+20 diopters. Gwideman (talk) 23:29, 15 October 2017 (UTC)

The source cited does not say whether it is giving the refractive power of the relaxed eye (minimum accommodation), but a quick Google search finds other sources that do give 60 D as the optical power of the relaxed eye, with accommodation adding up to about 10 D to this, for a young adult. I didn't see any that claimed optical power as low as 40–45 D for an actual eye. Be suspicious of naive analysis based on the diameter of the eyeball. The eye is not a thin lens attached to a ball filled with air, and one over the eye's diameter is not the optical power of the eye.--Srleffler (talk) 04:07, 16 October 2017 (UTC)