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

mirror A mirror, also known as a looking glass, is an object that Reflection (physics), reflects an image. Light that bounces off a mirror forms an image of whatever is in front of it, which is then focused through the lens of the eye or a camera ...

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

History

Ancient Texts

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

ancient Greece Ancient Greece () was a northeastern Mediterranean civilization, existing from the Greek Dark Ages of the 12th–9th centuries BC to the end of classical antiquity (), that comprised a loose collection of culturally and linguistically r ...

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

Euclid Euclid (; ; 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 geometry that largely domina ...

, 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 (; ; ) was a Greek scholar and mathematician who lived in Alexandria, Egypt. He edited and arranged Euclid's '' Elements'' and wrote commentaries on works by Euclid and Ptolemy. His daughter Hypatia also won fame as a mathema ...

. 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 (; , , also known as Heron of Alexandria ; probably 1st or 2nd century AD) was a Greek mathematician and engineer who was active in Alexandria in Egypt during the Roman era. He has been described as the greatest experimental ...

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

Ptolemy Claudius Ptolemy (; , ; ; – 160s/170s AD) was a Greco-Roman mathematician, astronomer, astrologer, geographer, and music theorist who wrote about a dozen scientific treatises, three of which were important to later Byzantine science, Byzant ...

. 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 spoken by the Latins (Italic tribe), Latins in Latium (now known as Lazio), the lower Tiber area aroun ...

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 princ ...

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

Book of Optics The ''Book of Optics'' (; or ''Perspectiva''; ) is a seven-volume treatise on optics and other fields of study composed by the medieval Arab scholar Ibn al-Haytham, known in the West as Alhazen or Alhacen (965–c. 1040 AD). The ''Book ...

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

Roger Bacon Roger Bacon (; or ', also '' Rogerus''; ), also known by the Scholastic accolades, scholastic accolade ''Doctor Mirabilis'', was a medieval English polymath, philosopher, scientist, theologian and Franciscans, Franciscan friar who placed co ...

, who cites him by name. 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. This phenomenon commonly affects lenses and curved mirrors, as these components are often shaped in a spherical ...

. 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 transmission medium, 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 commo ...

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

lens A lens is a transmissive optical device that 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 (14 April 112611 December 1198), archaically Latinization of names, Latinized as Averroes, was an Arab Muslim polymath and Faqīh, jurist from Al-Andalus who wrote about many subjects, including philosophy, theology, medicine, astron ...

' 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 BN, Bn or bn may refer to: Businesses and organizations Arts and media * RTV BN, a Bosnian Serb broadcaster * Bandai Namco, a gaming and entertainment conglomerate * Barnes & Noble, an American chain of bookstores * BN (band), Belarusian rock ban ...

''Optics'').

Renaissance

16th-century Jewish-Ferraresi physicist Rafael Mirami wrote a treatise on the subject, ''Compendiosa introduttione alla prima parte della specularia'', which became influential in a revival of the field, and contributed towards

Pope Gregory XIII Pope Gregory XIII (, , born Ugo Boncompagni; 7 January 1502 – 10 April 1585) was head of the Catholic Church and ruler of the Papal States from 13 May 1572 to his death in April 1585. He is best known for commissioning and being the namesake ...

's astronomical calculations that led to the creation of the

Gregorian Calendar The Gregorian calendar is the calendar used in most parts of the world. It went into effect in October 1582 following the papal bull issued by Pope Gregory XIII, which introduced it as a modification of, and replacement for, the Julian cale ...

Catoptric telescopes

The first practical catoptric

telescope A telescope is a device used to observe distant objects by their emission, Absorption (electromagnetic radiation), absorption, or Reflection (physics), reflection of electromagnetic radiation. Originally, it was an optical instrument using len ...

(the " Newtonian reflector") was built by

Isaac Newton Sir Isaac Newton () was an English polymath active as a mathematician, physicist, astronomer, alchemist, theologian, and author. Newton was a key figure in the Scientific Revolution and the Age of Enlightenment, Enlightenment that followed ...

as a solution to the problem of

chromatic aberration In optics, chromatic aberration (CA), also called chromatic distortion, color aberration, color fringing, or purple fringing, is a failure of a lens to focus all colors to the same point. It is caused by dispersion: the refractive index of the ...

exhibited in telescopes using lenses as objectives ( dioptric telescopes).

References

Bibliography