Catoptrics (from grc-gre, κατοπτρικός ''katoptrikós'', "specular", from grc-gre, κάτοπτρον ''katoptron'' "mirror") deals with the phenomena of reflected light and image-forming optical systems using

mirror A mirror or looking glass is an object that reflects an image. Light that bounces off a mirror will show an image of whatever is in front of it, when focused through the lens of the eye or a camera. Mirrors reverse the direction of the im ...

s. A catoptric system is also called a ''catopter'' (''catoptre'').

Ancient texts

''Catoptrics'' is the title of two texts from

ancient Greece Ancient Greece ( el, Ἑλλάς, Hellás) was a northeastern Mediterranean civilization, existing from the Greek Dark Ages of the 12th–9th centuries BC to the end of classical antiquity ( AD 600), that comprised a loose collection of cu ...

: *The Pseudo-Euclidean ''Catoptrics''. This book is attributed to

Euclid Euclid (; grc-gre, Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the '' Elements'' treatise, which established the foundations of ...

, although the contents are a mixture of work dating from Euclid's time together with work which dates to the Roman period., accessed 31 January 2013 It has been argued that the book may have been compiled by the 4th century mathematician

Theon of Alexandria Theon of Alexandria (; grc, Θέων ὁ Ἀλεξανδρεύς; 335 – c. 405) was a Greek scholar and mathematician who lived in Alexandria, Egypt. He edited and arranged Euclid's '' Elements'' and wrote commentaries on w ...

. The book covers the mathematical theory of mirrors, particularly the images formed by plane and spherical concave mirrors. *Hero's ''Catoptrics''. Written by

Hero of Alexandria Hero of Alexandria (; grc-gre, Ἥρων ὁ Ἀλεξανδρεύς, ''Heron ho Alexandreus'', also known as Heron of Alexandria ; 60 AD) was a Greek mathematician and engineer who was active in his native city of Alexandria, Roman Egypt. H ...

, this work concerns the practical application of mirrors for visual effects. In the Middle Ages, this work was falsely ascribed to

Ptolemy Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of importanc ...

. It only survives in a

Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through ...

translation.A. Mark Smith, (1999), ''Ptolemy and the Foundations of Ancient Mathematical Optics'', pages 16-17. American Philosophical Society. The Latin translation of

Alhazen Ḥasan Ibn al-Haytham, Latinized as Alhazen (; full name ; ), was a medieval mathematician, astronomer, and physicist of the Islamic Golden Age from present-day Iraq.For the description of his main fields, see e.g. ("He is one of the prin ...

's (Ibn al-Haytham) main work, ''

Book of Optics The ''Book of Optics'' ( ar, كتاب المناظر, Kitāb al-Manāẓir; la, De Aspectibus or ''Perspectiva''; it, Deli Aspecti) is a seven-volume treatise on optics and other fields of study composed by the medieval Arab scholar Ibn al- ...

'' (''Kitab al-Manazir''), exerted a great influence on Western science: for example, on the work of

Roger Bacon Roger Bacon (; la, Rogerus or ', also '' Rogerus''; ), also known by the scholastic accolade ''Doctor Mirabilis'', was a medieval English philosopher and Franciscan friar who placed considerable emphasis on the study of nature through emp ...

, who cites him by name., passim His research in catoptrics (the study of optical systems using mirrors) centred on spherical and parabolic mirrors and

spherical aberration In optics, spherical aberration (SA) is a type of aberration found in optical systems that have elements with spherical surfaces. Lenses and curved mirrors are prime examples, because this shape is easier to manufacture. Light rays that strik ...

. He made the observation that the ratio between the angle of incidence and

refraction In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomen ...

does not remain constant, and investigated the magnifying power of a

lens A lens is a transmissive optical device which focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (''elements ...

. His work on catoptrics also contains the problem known as " Alhazen's problem". Alhazen's work influenced

Averroes Ibn Rushd ( ar, ; full name in ; 14 April 112611 December 1198), often Latinized as Averroes ( ), was an Andalusian polymath and jurist who wrote about many subjects, including philosophy, theology, medicine, astronomy, physics, psy ...

' writings on optics, and his legacy was further advanced through the 'reforming' of his ''Optics'' by Persian scientist Kamal al-Din al-Farisi (d. ca. 1320) in the latter's ''Kitab Tanqih al-Manazir'' (''The Revision of'' bn al-Haytham's''Optics'').

Catoptric telescopes

The first practical catoptric

telescope A telescope is a device used to observe distant objects by their emission, absorption, or reflection of electromagnetic radiation. Originally meaning only an optical instrument using lenses, curved mirrors, or a combination of both to obse ...

(the " Newtonian reflector") was built by

Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, Theology, theologian, and author (described in his time as a "natural philosophy, natural philosopher"), widely ...

as a solution to the problem of

chromatic aberration In optics, chromatic aberration (CA), also called chromatic distortion and spherochromatism, is a failure of a lens to focus all colors to the same point. It is caused by dispersion: the refractive index of the lens elements varies with the w ...

exhibited in telescopes using lenses as objectives (

dioptric Dioptrics is the branch of optics dealing with refraction, similarly the branch dealing with mirrors is known as catoptrics. Dioptrics is the study of the refraction of light, especially by lenses. Telescopes that create their image with an ob ...

telescopes).

References

Bibliography

* * * * * {{Ancient Greek mathematics Optical telescopes

Ancient texts

Catoptric telescopes

See also

References

Bibliography