# Matthiessen's ratio

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Type of optic ratio

For the electron mobility rule, see [Matthiessen's rule](/source/Matthiessen's_rule).

In [optics](/source/Optics), **Matthiessen's ratio** is the ratio between the distance from the centre of the [lens](/source/Lens_(anatomy)) to the [retina](/source/Retina), versus the lens [radius](/source/Radius) in fish and other [aquatic animals](/source/Aquatic_animals). It was found to be constant at 2.55 in most fishes, while the value may decrease from as high as 3.6 to 2.3 in some fishes.

## Background

Wilhelm Matthiessen (1840–1890) was a German physiologist and anatomist who made pioneering studies of the eye, particularly fish eye optics. His work in the 1880s laid the foundation for understanding the geometric optics of spherical lenses in aquatic animals.[1][2] It provides a key metric for estimating focal length and visual capabilities without invasive measurements, widely used in aquatic animal vision research.[3]

## Description

It defines that the ratio of the distance from the center of the [lens](/source/Lens) to the [retina](/source/Retina) (posterior nodal distance) to the lens radius in fish and other aquatic animals.[4] It was found to be constant at 2.55 in most fishes, meaning the size of the eye remains constant.[5] However, the value may decrease from as high as 3.6 to 2.3, decreasing the [focal ratio](/source/Focal_ratio) of the [lens](/source/Lens_(optics)). A higher focal ratio is thought to compensate for the relatively high Matthiessen's ratio brought about by constraints of small eye size during early development. This provides a means for [larval](/source/Larva) fish to focus images from different distances, before the ability to [accommodate](/source/Accommodation_(eye)) is gained.[1] Most bony fish adhere to the ratio, with a few exceptions.[6] Larval fish start with a higher ratio (~3.6) that decreases during development to around 2.3–2.6 as the eye matures and gains accommodation ability.[7] The fish lenses have a [refractive index](/source/Refractive_index) gradient that varies from about 1.52 in the centre to 1.33 at its surface.[3]

## See also

- [Digital Fish Library](/source/Digital_Fish_Library)

- [Fish development](/source/Fish_development)

- [Operculum papillare](/source/Operculum_papillare)

- [Photophore](/source/Photophore)

- [Sensory systems in fish](/source/Sensory_systems_in_fish)

- [Stylophthalmine trait](/source/Stylophthalmine_trait)

- [Vision in fish](/source/Vision_in_fish)

- [Visual perception](/source/Visual_perception)

## References

1. ^ [***a***](#cite_ref-shand_1-0) [***b***](#cite_ref-shand_1-1) Shand, J.; K. B Døving; S. P Collin (1999). ["Optics of the developing fish eye: comparisons of Matthiessen's ratio and the focal length of the lens in the black bream Acanthopagrus butcheri (Sparidae, Teleostei)"](https://doi.org/10.1016%2FS0042-6989%2898%2900215-6). *Vision Research*. **39** (6): 1071–1078. [doi](/source/Doi_(identifier)):[10.1016/S0042-6989(98)00215-6](https://doi.org/10.1016%2FS0042-6989%2898%2900215-6). [ISSN](/source/ISSN_(identifier)) [0042-6989](https://search.worldcat.org/issn/0042-6989). [PMID](/source/PMID_(identifier)) [10343827](https://pubmed.ncbi.nlm.nih.gov/10343827). [S2CID](/source/S2CID_(identifier)) [8525655](https://api.semanticscholar.org/CorpusID:8525655).

1. **[^](#cite_ref-2)** Matthiessen, Ludwig (1 December 1882). ["Ueber die Beziehungen, welche zwischen dem Brechungsindex des Kerncentrums der Krystalllinse und den Dimensionen des Auges bestehen"](https://doi.org/10.1007/BF01802978). *Archiv für die gesamte Physiologie des Menschen und der Tiere* (in German). **27** (1): 510–523. [doi](/source/Doi_(identifier)):[10.1007/BF01802978](https://doi.org/10.1007%2FBF01802978). [ISSN](/source/ISSN_(identifier)) [1432-2013](https://search.worldcat.org/issn/1432-2013).

1. ^ [***a***](#cite_ref-Ponder_3-0) [***b***](#cite_ref-Ponder_3-1) Winston Frank Ponder, David R. Lindberg, Juliet Mary Ponder (2019). *Biology and Evolution of the Mollusca, Volume 1*. CRC Press. [ISBN](/source/ISBN_(identifier)) [978-1-351-11565-0](https://en.wikipedia.org/wiki/Special:BookSources/978-1-351-11565-0).{{[cite book](https://en.wikipedia.org/wiki/Template:Cite_book)}}: CS1 maint: multiple names: authors list ([link](https://en.wikipedia.org/wiki/Category:CS1_maint:_multiple_names:_authors_list))

1. **[^](#cite_ref-4)** ["Evolution of eyes"](https://studylib.net/doc/8368775/the-evolution-of-eyes---redwood-center-for-theoretical-neuroscience). p. 25. Retrieved 1 June 2025.

1. **[^](#cite_ref-5)** *Coral Reef Fishes Dynamics and Diversity in a Complex Ecosystem*. Elsevier Science. 2006. p. 127. [ISBN](/source/ISBN_(identifier)) [978-0-123-73609-3](https://en.wikipedia.org/wiki/Special:BookSources/978-0-123-73609-3).

1. **[^](#cite_ref-6)** Ivan R. Schwab, Richard R. Dubielzig, Charles Schobert (2012). *Evolution's Witness How Eyes Evolved*. [Oxford University Press](/source/Oxford_University_Press). p. 88-89. [ISBN](/source/ISBN_(identifier)) [978-0-195-36974-8](https://en.wikipedia.org/wiki/Special:BookSources/978-0-195-36974-8).{{[cite book](https://en.wikipedia.org/wiki/Template:Cite_book)}}: CS1 maint: multiple names: authors list ([link](https://en.wikipedia.org/wiki/Category:CS1_maint:_multiple_names:_authors_list))

1. **[^](#cite_ref-7)** "Optics of the developing fish eye: comparisons of Matthiessen's ratio". *Vision Res*. **39** (6): 1071–8. 1999. [doi](/source/Doi_(identifier)):[10.1016/s0042-6989(98)00215-6](https://doi.org/10.1016%2Fs0042-6989%2898%2900215-6). [PMID](/source/PMID_(identifier)) [10343827](https://pubmed.ncbi.nlm.nih.gov/10343827).

[Portals](https://en.wikipedia.org/wiki/Wikipedia:Contents/Portals):
- [Fish](https://en.wikipedia.org/wiki/Portal:Fish)
- [Oceans](https://en.wikipedia.org/wiki/Portal:Oceans)
- [Water](https://en.wikipedia.org/wiki/Portal:Water)
- [Science](https://en.wikipedia.org/wiki/Portal:Science)
- [Technology](https://en.wikipedia.org/wiki/Portal:Technology)

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