{{Short description|Type of optic ratio}} {{For|the electron mobility rule|Matthiessen's rule}} In [[optics]], '''Matthiessen's ratio''' is the ratio between the distance from the centre of the [[Lens (anatomy)|lens]] to the [[retina]], versus the lens [[radius]] in fish and other [[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.<ref name='shand'>{{Cite journal | issn = 0042-6989 | volume = 39 | issue = 6 | pages = 1071–1078 | last = Shand | first = J. |author2=K. B Døving |author3=S. P Collin | title = 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) | journal = Vision Research | year = 1999 | pmid = 10343827 | doi = 10.1016/S0042-6989(98)00215-6 | s2cid = 8525655 | doi-access = free }}</ref><ref>{{cite journal |last=Matthiessen |first=Ludwig |date=1 December 1882 |title=Ueber die Beziehungen, welche zwischen dem Brechungsindex des Kerncentrums der Krystalllinse und den Dimensionen des Auges bestehen |url=https://doi.org/10.1007/BF01802978 |journal=Archiv für die gesamte Physiologie des Menschen und der Tiere |language=de |volume=27 |issue=1 |pages=510–523 |doi=10.1007/BF01802978 |issn=1432-2013}}</ref> It provides a key metric for estimating focal length and visual capabilities without invasive measurements, widely used in aquatic animal vision research.<ref name="Ponder">{{cite book|title=Biology and Evolution of the Mollusca, Volume 1|author=Winston Frank Ponder, David R. Lindberg, Juliet Mary Ponder|year=2019|isbn=978-1-351-11565-0|publisher=CRC Press}}</ref>
== Description == It defines that the ratio of the distance from the center of the [[lens]] to the [[retina]] (posterior nodal distance) to the lens radius in fish and other aquatic animals.<ref>{{cite web|url=https://studylib.net/doc/8368775/the-evolution-of-eyes---redwood-center-for-theoretical-neuroscience|title=Evolution of eyes|page=25|access-date=1 June 2025}}</ref> It was found to be constant at 2.55 in most fishes, meaning the size of the eye remains constant.<ref>{{cite book|title=Coral Reef Fishes Dynamics and Diversity in a Complex Ecosystem|year=2006|page=127|isbn=978-0-123-73609-3|publisher=Elsevier Science}}</ref> However, the value may decrease from as high as 3.6 to 2.3, decreasing the [[focal ratio]] of the [[Lens (optics)|lens]]. 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 [[larva]]l fish to focus images from different distances, before the ability to [[Accommodation (eye)|accommodate]] is gained.<ref name="shand"/> Most bony fish adhere to the ratio, with a few exceptions.<ref>{{cite book|title=Evolution's Witness How Eyes Evolved|author=Ivan R. Schwab, Richard R. Dubielzig, Charles Schobert|year=2012|isbn=978-0-195-36974-8|publisher=[[Oxford University Press]]|page=88-89}}</ref> 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.<ref>{{cite journal|journal=Vision Res|date=1999|volume=39|issue=6|pages=1071–8|doi=10.1016/s0042-6989(98)00215-6|title=Optics of the developing fish eye: comparisons of Matthiessen's ratio|pmid=10343827 }}</ref> The fish lenses have a [[refractive index]] gradient that varies from about 1.52 in the centre to 1.33 at its surface.<ref name="Ponder"/>
== See also == {{cmn| *[[Digital Fish Library]] *[[Fish development]] *[[Operculum papillare]] *[[Photophore]] *[[Sensory systems in fish]] *[[Stylophthalmine trait]] *[[Vision in fish]] *[[Visual perception]] }}
== References == {{reflist}}
{{Portal bar|Fish|Oceans|Water|Science|Technology}} [[Category:Fish anatomy]] [[Category:Eye]]