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Infinity-correcting adapters tend to incorporate a weak teleconverter usually.

It would appear that a thick, planar optical glass window is also capable of lengthening back focus - and would probably introduce less new problems.

Why is this not done in practice?

If there is a reason this is not done in commercial, DSLR oriented adapters, would that same reason also make this an unsuccessful solution for eg adapting X-ray relay lenses to DSLMs (think glueing something like an Edmund #38-055 onto the back of the lens)?

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  • \$\begingroup\$ I'm not an expert in optics, but โ€” how would a plane of glass differ from... just nothing? \$\endgroup\$
    – mattdm
    Dec 25, 2019 at 19:26
  • \$\begingroup\$ @ mattdm - An optical flat will actually shorten the focal length (a smidgeon). \$\endgroup\$ Dec 25, 2019 at 22:05
  • \$\begingroup\$ Might be my misunderstanding... textbooks suggest that such a flat will set "the image further back"? \$\endgroup\$ Dec 25, 2019 at 23:42
  • \$\begingroup\$ @ rackabdbibenan -- I apologies - re-checking old class note - you are correct - I was wrong - an optical flat will set the image back a smidgeon - like a view under water - objects appear nearer, \$\endgroup\$ Dec 26, 2019 at 1:01

3 Answers 3

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Camera lenses are converging lenses, meaning they have positive power. A simple convex lens will do this job, however, the image is flawed. I am talking chromatic aberration whereby each color will come to a focus at a different distance downstream of the lens.

Now a negative lens diverges and a positive lens converges. Additionally they display opposite chromatic aberrations. The lens maker corrects by combining strong positive lens elements with weak negatives. The result is an achromatic (without color error), well nearly but not perfection.

The focal length is a measurement taken when the lens is imaging a far distant target. This will be the shortest back-focus. If the lens and its mounting are mismatched, the infinity focus (the shortest back-focus) may not reach film or digital sensor. To correct, we must somehow shorten the distance lens-to-sensor/film or lengthen the back focus.

The only way to lengthen the back focus is to impose a weak negative (diverging) lens. This procedure actually lengthens the focal length a smidgen. Now a single element negative will do this trick, however, such a lash-up adds to the chromatic aberration.

The countermeasure is a doublet, one with negative power and the other with positive power. The powers are adjusted so the combination has negative power. This is a common trick used in telescopes, called a โ€œBarlowโ€. This classic supplemental lens array is exactly what is needed to lengthen out a back-focus error.

Incidentally, an optical flat, either before, in-between, or behind the lens elements of a camera lens will microscopically lengthen the focal length so what you propose could be accomplished provided the optical flat was quite thick. Sorry this original post was in error. On with my duce cap, in the corner for two hours.

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  • \$\begingroup\$ But the optical flat would also introduce chromatic aberration? \$\endgroup\$
    – xenoid
    Dec 26, 2019 at 10:46
  • \$\begingroup\$ @ xenoid _ I was sleeping in class when they discussed that an optical flat would lengthen the focal length. Yes it would induce chromatic aberration. I once used very thick, dyed in the mass glass filters (had a set of various colors). They were about 12mm in thickness. I did not notice any focal length shift or induced aberrations. I used them only for black & white film. \$\endgroup\$ Dec 26, 2019 at 14:18
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Because in many cases the flat glass needed to lengthen the back focus by the needed amount would need to be thicker than the entire registration distance.

The effect of flat glass is so miniscule that it would take glass thicker than the space available to get the desired additional back focus distance for most applications.

Flat glass would also introduce many of the same issues that a weak diverging lens would, to pretty much the same degree as the amount of distance it lengthens back focus.

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It would appear that a thick, planar optical glass window is also capable of lengthening back focus - and would probably introduce less new problems.

Why is this not done in practice?

Because it won't work. It won't lengthen the back focus enough. That is, a flat optical element shifts the focus by an amount less than the thickness of that flat element.

In the following diagram, a marginal ray (the red ray) from the edge of the lens's exit pupil of diameter d is focused at the back-focus distance b. That ray approaches at an angle ๐œƒโ‚.

Diagram showing focus shift for different refractive indices

But that lens is shifted too far from the image sensor by an amount t, so that the lens can't achieve infinity focus. So inserting a flat element of thickness t with refractive index nโ‚‚ will cause a shift in the back focus distance towards the image sensor by an amount s, because of Snell's Law: sin(๐œƒโ‚) = nย sin(๐œƒโ‚‚).

For convenience's sake, I will normalize the refractive index with respect to air (nโ‚) with: n = nโ‚‚/nโ‚.

  • The dashed red ray is the original path if the optical flat were not present, or alternately, is the path the ray would follow if the glass had the same refractive index as the air surrounding it (if n = 1).
  • The black ray is the desired path that would shift the back focus distance by t. But in order to achieve that, the refractive index would have to be infinite. This is undesirable:
    • A material with infinite refractive index has a reflectivity of 1, meaning that it is a mirror, and admits no light through the air/material interface.
    • This can also be understood by remembering that the refractive index of a material is defined as the ratio of the speed of light in a vacuum to the phase velocity of light in that material: n = c/v. In order for n = โˆž, v must equal zero. Thus, light does not travel through the material.
  • The blue ray is the light path for typical optical materials (n > 1, usually in the neighborhood of 1.5ย โ€“ย 1.6, up to around 1.7 or 1.8 for lead glass). Geometrically, you can see that for finite (and realistic, positive) values of n, the focus shift distance s will always be less than t.

Mathematically, the amount of shift s is given by:

Equation for focus shift

where m = d / (2ย b) = tan(๐œƒโ‚). For a lens focused at infinity, this is just the exit pupil half-diameter divided by the focal length of the lens.

You can see from the equation that the radical in the denominator is always greater than 1, for real-world optical glass elements with refractive index greater than 1. Thus, the entire expression in the parentheses that multiplies t is positive and less than 1. So the shift s is always less than t for real world materials.


I keep saying "real world materials", because there are some metamaterials that have been built that have a negative refractive index, which would theoretically replace the need for concave (diverging) elements. Most of the negative-index metamaterials constructed so far are not transparent to visible light.

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  • \$\begingroup\$ I should caveat my answer with the assumption that the thickness of the flat is no more than the amount the lens is shifted too far forward (i.e., the optical flat does not protrude forward into the rear of the lens (for lenses with recessed rear optical elements), or into the camera body / mirror box further than the lens bayonet mount would protrude). You could certainly intrude into the camera body (for instance, by performing a mirror lock-up before attaching/inserting the optical flat). But that's a very special-case scenario, and would not be a general solution for most retail photo gear \$\endgroup\$
    – scottbb
    Jan 8, 2020 at 3:01
  • \$\begingroup\$ Wonder if it could be a solution for eg adapting X-ray or ENG camera lenses to mirrorless, with a flint glass cylinder going in to 2mm from the shutter :) \$\endgroup\$ Jan 9, 2020 at 0:22
  • \$\begingroup\$ @rackandboneman I don't know anything about x-ray lenses; correct me if I'm wrong, but don't ENG lenses have something like 48mm flange focus distance? If that's the case, there's plenty of room to mount just a basic mount adapter to a typical mirrorless body of 16โ€“20mm FFD. No compensating glass needed. \$\endgroup\$
    – scottbb
    Jan 9, 2020 at 2:13

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