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A fact from this article was featured on Wikipedia's Main Page in the On this day section on January 23, 2021 and January 23, 2023.

Missing: Resolution limit

Abbe's most important contribution: The finding that the resolution of the microscope depends on the numerical aperture and the wavelength, but not on the magnification. This is not yet mentioned in the article. --Millencolin (talk) 19:26, 13 October 2009 (UTC)[reply]

Could someone please define NA and lambda in the formula?128.220.117.40 (talk) 00:59, 23 June 2013 (UTC)[reply]

I've added citations to numerous articles authored by Abbe. Abbe define NA and new that NA and resolution were inversely proportional, as he stated in his Contribution to the Theory of the Microscope paper. However at that time he didn't present the analytical relation, d = lambda/(2NA). The first appearance of that EQ by Abbe was in his 1882 paper, The Relation of Aperture and Power in the Microscope (continued). Where he stated that he has found this to be theoretically and experimentally true.

However, the first appearance(that I could find) and theoretical derivation of the d = lambda/(2*NA) formula was in a paper by Helmholtz in 1874, titled, "On the Limits of the Optical Capacity of the Microscope", translated by Fripp. In this paper Helmhotlz stated, that this formula was first shown by Lagrange, probably at least 30 years prior but wasn't widely read, I haven't found this paper and it's probably in French but remember diffraction theory was pretty well developed by 1870 thanks to the work of Fresnel. Gfutia (talk) 06:12, 5 January 2011 (UTC)[reply]

Translation

I'm German and I'd translate 'Über die Grenzen der geometrischen Optik' as "About the limits of...", rather than "Beyond...". I've no access to the full text, though, so I can't verify.

—— (1878). "Über die Grenzen der geometrischen Optik" [Beyond the Limits of Geometric Optics]. Jenaische Zeitschrift für Naturwissenschaft [Jenaische Journal of Natural Science] (in German) (Jena, Germany: Verlag Von Gustav Fischer): 71–109.

You are correct. In this context, a scientific paper- Usually translated as the somewhat more formal "Concerning."MikroSammler (talk) 21:25, 3 May 2017 (UTC)[reply]

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 == Missing: Resolution limit ==
@@ Line 17: / Line 13: @@
 Abbe's most important contribution: The finding that the resolution of the microscope depends on the numerical aperture and the wavelength, but not on the magnification. This is not yet mentioned in the article.
 --[[User:Millencolin|Millencolin]] ([[User talk:Millencolin|talk]]) 19:26, 13 October 2009 (UTC)
+Could someone please define NA and lambda in the formula?[[Special:Contributions/128.220.117.40|128.220.117.40]] ([[User talk:128.220.117.40|talk]]) 00:59, 23 June 2013 (UTC)
+I've added citations to numerous articles authored by Abbe. Abbe define NA and new that NA and resolution were inversely proportional, as he stated in his Contribution to the Theory of the Microscope paper. However at that time he didn't present the analytical relation, d = lambda/(2NA). The first appearance of that EQ by Abbe was in his 1882 paper, The Relation of Aperture and Power in the Microscope (continued). Where he stated that he has found this to be theoretically and experimentally true.
+However, the first appearance(that I could find) and theoretical derivation of the d = lambda/(2*NA) formula was in a paper by Helmholtz in 1874, titled, "[http://books.google.com/books?id=4r4EAAAAQAAJ&dq=Journal%20of%20the%20Royal%20Microscopical%20Society%20%201881&pg=PA460#v=onepage&q&f=false On the Limits of the Optical Capacity of the Microscope]", translated by Fripp. In this paper Helmhotlz stated, that this formula was first shown by Lagrange, probably at least 30 years prior but wasn't widely read, I haven't found this paper and it's probably in French but remember diffraction theory was pretty well developed by 1870 thanks to the work of Fresnel.
+[[User:Gfutia|Gfutia]] ([[User talk:Gfutia|talk]]) 06:12, 5 January 2011 (UTC)
+== Translation ==
+I'm German and I'd translate 'Über die Grenzen der geometrischen Optik' as "About the limits of...", rather than "Beyond...". I've no access to the full text, though, so I can't verify.
+ —— (1878). "Über die Grenzen der geometrischen Optik" [Beyond the Limits of Geometric Optics]. Jenaische Zeitschrift für Naturwissenschaft [Jenaische Journal of Natural Science] (in German) (Jena, Germany: Verlag Von Gustav Fischer): 71–109.
+You are correct.  In this context, a scientific paper- Usually translated as the somewhat more formal "Concerning."[[User:MikroSammler|MikroSammler]] ([[User talk:MikroSammler|talk]]) 21:25, 3 May 2017 (UTC)