Talk:Thin lens

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Should this be part of Lens (optics)?[edit]

Hi, I don't see why this needs to be a separate article as Lens (optics) covers most of this. All of the equations in that article besides the Lensmaker's equation with thickness d as well as nearly all the text except the section on Aberrations is valid for or based on thin lens equations. The drawings seem more informative too.

I can imagine the reference to Ray transfer matrix analysis, if combined with more material as possibly the beginning of a separately needed article.

Consider the disambiguation page at Lens as a map of meanings, types and uses of lenses and try to think of why it should link here also, such as

  • What properties are unique to thin lenses?
    • They will lack some geometrical problems like spherical aberration
    • But they will still have chromatic aberration
    • They will have insertion loss due to surface reflection
      • For a constant focal length, surface reflection increases for thinner lenses because the refractive index needed increases
    • Also probably coma, if we can't use the paraxial approximation
  • Should the paraxial approximation be a central assumption?
  • Copy half the material in the article Lens (optics) with some slight modifications
  • How thin is thin enough?

Otherwise it would be better merged as some special section(s) and subsections in Lens (optics). --Dgroseth (talk) 05:03, 18 July 2009 (UTC)

I think this proposal needs some more thought, and some input from other editors. In optics, a "thin lens" is not so much a type of lens, as an approximation used in modeling real lenses. A "thin lens" is infinitely thin. This model simplifies the treatment of real physical lenses by ignoring effects due to their thickness. This model is extremely important in optics. I'm not sure it is best handled by merging the two articles. Perhaps the contents of this article should be adjusted instead, to focus on the thin lens model as an approximation used in optics, rather than a type of lens that happens to be thin. --Srleffler (talk) 04:52, 19 July 2009 (UTC)

ignore surfaces or nodal space ?[edit]

The article currently states that the "thin lens approximation" ignores the distance between the surfaces of the lens, whereas several sources indicate that the nodal space (distance between front and last principal planes) is disregarded :

  • Melles Griot states clearly "With a real lens of finite thickness, the image distance, object distance, and focal length are all referenced to the principal points, not to the physical center of the lens. By neglecting the distance between the lens' principal points, known as the hiatus, s + s" becomes the object-to-image distance. This simplification, called the thin-lens approximation, can speed up calculation when dealing with simple optical systems."
  • Greivenkamp defines "A thin lens is the most common element used in first-order layout. This idealized element has an optical power but no thickness and can be considered as a single refracting surface separating two spaces with the same index (usually air). The principal planes and nodal points are located at the lens." --Redbobblehat (talk) 19:37, 11 August 2009 (UTC)
Both ways of describing it are correct. Optically, a thick lens behaves like a thin lens of the same focal length, except that one measures distances from the principal planes rather than from the centre of the lens. Physically, though, you don't get a thin lens by chopping out the distance between the principal planes. Rather, you get it by letting the physical thickness of the lens go to zero. A thick lens goes to a thin one in this limit. --Srleffler (talk) 02:27, 12 August 2009 (UTC)
I don't understand what you mean by "letting the physical thickness of the lens go to zero". I realise that thin lens approximation is a geometrical idealisation/simplification, but comparison to Fresnel lens design is very tempting. This paper makes several references to "thinness" - though not claiming that fresnels actually realise the ideal thin lens, the advantages of approximating the ideal surely cannot be irrelevant ? --Redbobblehat (talk) 16:37, 4 February 2011 (UTC)
Sorry for the confusing terminology. Phrasing like "letting x go to zero" is used in mathematics and physics to describe the process of taking a limit. The idea here is to imagine starting with a thick lens and gradually making it thinner while keeping the focal length the same. As the lens gets thinner, the principal planes move toward one another. If the lens's thickness becomes infinitely small, the principal planes coincide with the location of the lens.
Fresnel lenses are generally much worse than conventional lenses. They are fine when you don't want to form an image, and acceptable when you need a crummy lens that is big and light, thin, or cheap. The ideal thin lens is an unphysical idealization; something that cannot be achieved in the real world. It is good not because it is thin, but because the model presumes all parallel rays will be brought to the same focus, regardless where they strike the lens. Lenses with spherical surfaces don't do this (they suffer from spherical aberration, among other things.--Srleffler (talk) 03:35, 5 February 2011 (UTC)

centre of the lens[edit]

When I come across the phrase "centre of the lens" in optics parlance, it seems to be an infallible clue that the thin lens model is being used. It seems to me to be a rather useful clue and worthy of mention here ? Unless I am completely wrong, I would like to suggest creating the centre of the lens link and #REDIRECTing it to this article. Obviously this article should also mention and explain the phrase. In my ignorance I can't help but think that this "centre of the lens" concept might be the nub of "thin lens approximation" ? --Redbobblehat (talk) 16:04, 4 February 2011 (UTC)

Perhaps something along the lines of : In the thin lens model, the centre of the lens is a single geometrical point on the axis used to represent the location of the nodal points, principal points, entrance and exit pupils, aperture stop ... etc ? Because all these things are 'compressed' into one all purpose point, the usefulness of thin lens model is limited to... and so on. Perhaps someone more knowledgeable could 'tidy up' or 'pick up' this line of reasoning and include it in the article ? --Redbobblehat (talk) 16:04, 4 February 2011 (UTC)

You're thinking along the right lines here. In fact optical centre redirects to a passage that reads, in part "For a thin lens in air, the principal planes both lie at the location of the lens. The point where they cross the optical axis is sometimes misleadingly called the optical centre of the lens. Note, however, that for a real lens the principal planes do not necessarily pass through the centre of the lens, and in general may not lie inside the lens at all."--Srleffler (talk) 03:20, 5 February 2011 (UTC)
Would it be better to route centre of the lens and optical centre to an explanation/definition in this, the "thin lens" article ? The way I see it is the "thin lens model" forms the 'chassis' for a number of other, more specialized 'modules' : Newtonian conjugates (?) is one, Gaussian cardinals is another. The main purpose of Gauss's cardinal contraption, is to 'upgrade' the thin lens model by tackling the "centre of the lens" limitation (and some other bells and whistles ;). In the process, it becomes slightly more complicated, but it is still very much an extension of the thin lens model. Sometimes understanding the thin lens model - its conventions and limitations - is all the reader needs to know, so complicating it with gaussian or newtonian embellishments is unnecessary and unhelpful. So, digestible chunk 1 "get your head round the thin lens model" then go to digestible chunk 2 "how the gaussian model builds on the thin lens model"... etc. Does that make sense ? --Redbobblehat (talk) 05:44, 5 February 2011 (UTC)
I would add that I don't think the terms "centre of the lens" or "optical centre" are "misleading" if they are confined to the context of the thin lens model. Applied to other models they are annoyingly imprecise - but surely that's all the more reason to nail them down here, where they have legitimate - if limited - meaning ? I noticed recently that Nikon's lens glossary defines focal length as the "distance from the focal plane to the centre of the lens" (or similar) ... which - by invoking the thin lens model - is actually more specific than it first sounds! --Redbobblehat (talk) 05:44, 5 February 2011 (UTC)
The problem with "centre of the lens" is that it has no value even in the thin lens model, and actively misleads in any other case. The quote from the Nikon lens glossary is a perfect example: saying that focal length is the "distance from the focal plane to the centre of the lens" is completely wrong for most lenses. For a thin lens it is meaningless to talk about the "centre of the lens", since the lens is infinitely thin. The focal length of a thin lens is the distance from the lens to the focal plane.Srleffler (talk) 06:41, 5 February 2011 (UTC)
Hecht 2003 Optics pp.159-60 appears (I struggled to follow it) to be a proof that the "optical center" (from which "an off-axis paraxial ray emerges from the lens parallel to its incident direction") point coincides with the 'centre of symmetry'(?) between the surfaces of a simple bi-convex spherical ("constant radius") lens. He even includes (Fig 5.16) a photo of one! He also notes its 'value' : "it is particularly convenient to draw a ray through the center of the lens, which, because it is perpendicular to both surfaces, is undeviated." ... so that would be the principal ray ? which does seem to come in handy for conjugate heights, etc. But isn't this part of an esoteric debate about spherical aberration ? If the "thin lens" 'model' is a first-order approximation which ignores all the aberrations, it shouldn't be a problem here ? I suspect Hecht's intention is to show how surprisingly accurate this approximation can be - albeit in one special case. --Redbobblehat (talk) 19:30, 6 February 2011 (UTC)
For "optical centre of lens" see also [1] --Redbobblehat (talk) 22:11, 6 February 2011 (UTC)
The centre of a thin lens is the point where it intersects the axis. The nikon statement is perfectly accurate if we recognise that "the centre of the lens" includes (but doesn't differentiate) Gauss' principal points and nodal points. Wisniewski's data bears this out (compare specified focal length to distance between rear node and film plane). --Redbobblehat (talk) 19:30, 6 February 2011 (UTC)
I agree with you about the thin lens model forming a basis for understanding optics, which can be refined in steps by moving up to better approximations such as Gaussian optics. Optics is a tiered series of approximations, with the thin lens being an example of the lowest tier.--Srleffler (talk) 06:41, 5 February 2011 (UTC)
"Models" : I'm intrigued by how an opticist might use either the gaussian conjugate distances or the newtonian ones, depending on which gives the most efficient solution for a given task. Newton, it seems, was not very interested in the "centre of the lens"; his equations use the object-focus (x) and focus-image (x') distances (to show, for example, the special case of unit magnification when f = x = x' [see Fig 19]). The Gaussian and Newtonian conjugate "models" are not incompatible, but they are different. Nor is one "better" than the other. It may be more helpful to think of them as "modular" rather than "progressively refined"; sophistication is not a reliable indication of fitness for purpose. --Redbobblehat (talk) 19:30, 6 February 2011 (UTC)
By "model" I mean a geometrical figure which defines a bunch of variables so that algebraic equations can be derived from it and specific unknown values can be calculated. So the "conjugate model" gives rise to "conjugate equations", etc. Each model will have limitations, not least due to whichever "approximations" it employs (== which "aberrations" it ignores?), and conventions which govern its correct use. IMHO It seems quite important that a wikipedia article explicitly describes the purpose/uses and limitations of each model. --Redbobblehat (talk) 19:30, 6 February 2011 (UTC)

Goodman,D mentions a couple of possible specific meanings for "centre of the lens" : "A nodal ray is one that passes through the nodal points. Such a ray must cross the axis, and the point where it does so physically is sometimes called the lens center. In general, this point has no special properties. (Gauss suggested an alternate "lens center", the point midway between the principal points. Rotating a lens front to rear about this point would leave object and image positions and magnifications unchanged.)"[2] ... helpful ? --Redbobblehat (talk) 15:40, 12 February 2011 (UTC)