Catoptrics (from grc-gre, κατοπτρικός ''katoptrikós'', "specular", from grc-gre, κάτοπτρον ''katoptron'' "mirror") deals with the phenomena of
reflected light
Reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves. The ' ...
and
image-forming optical system
Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviole ...
s using
mirror
A mirror or looking glass is an object that Reflection (physics), 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 ...
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 cult ...
:
*The Pseudo-Euclidean ''Catoptrics''. This book is attributed to
Euclid
Euclid (; grc-gre, Wikt:Εὐκλείδης, Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the ''Euclid's Elements, Elements'' trea ...
, 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 works ...
.
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 Greece, Greek mathematician and engineer who was active in his native city of Alexandria, Roman Egy ...
, 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 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 the power of the ...
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 empiri ...
, 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 optical aberration, aberration found in optical systems that have elements with spherical surfaces. Lens (optics), Lenses and curved mirrors are prime examples, because this shape is easier to man ...
. 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 phenomeno ...
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 problem, also known as Alhazen's billiard problem, is a mathematical problem in geometrical optics first formulated by Ptolemy in 150 AD.
It is named for the 11th-century Arab mathematician Alhazen (''Ibn al-Haytham'') who presented a ...
".
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, psycholog ...
' writings on optics, and his legacy was further advanced through the 'reforming' of his ''Optics'' by Persian scientist
Kamal al-Din al-Farisi
Kamal may refer to:
*Kamal (name), a male given name and surname with multiple origins
*Kamal (navigation), a navigational instrument for measuring latitude
*Kamal, Jhapa, a rural municipality in Nepal
*Alfa Romeo Kamal, an SUV by Alfa Romeo
*Oper ...
(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
* RTV BN, a Bosnian Serb TV network
* Bangladesh Navy
* Barisan Nasional (also known as "National Front"), a political coalition in Malaysia
* Barnes & Noble, an American specialty retailer ...
''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 observe ...
(the "
Newtonian reflector
The Newtonian telescope, also called the Newtonian reflector or just a Newtonian, is a type of reflecting telescope invented by the English scientist Sir Isaac Newton, using a concave primary mirror and a flat diagonal secondary mirror. Newton' ...
") was built by
Isaac Newton
Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a "natural philosopher"), widely recognised as one of the grea ...
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 wave ...
exhibited in telescopes using lenses as
objective
Objective may refer to:
* Objective (optics), an element in a camera or microscope
* ''The Objective'', a 2008 science fiction horror film
* Objective pronoun, a personal pronoun that is used as a grammatical object
* Objective Productions, a Brit ...
s (
dioptric
Dioptrics is the branch of optics dealing with refraction, similarly the branch dealing with mirror
A mirror or looking glass is an object that Reflection (physics), reflects an image. Light that bounces off a mirror will show an image of ...
telescopes).
See also
*
Dioptrics
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 object ...
*
Catadioptrics
A catadioptric optical system is one where refraction and reflection are combined in an optical system, usually via lenses (dioptrics) and curved mirrors (catoptrics). Catadioptric combinations are used in focusing systems such as searchlights, he ...
*
Optical telescope
An optical telescope is a telescope that gathers and focuses light mainly from the visible part of the electromagnetic spectrum, to create a magnified image for direct visual inspection, to make a photograph, or to collect data through electro ...
*
List of telescope types
The following are lists of devices categorized as types of telescopes or devices associated with telescopes. They are broken into major classifications with many variations due to professional, amateur, and commercial sub-types. Telescopes can be ...
*
Image-forming optical system
In optics, an image-forming optical system is a system capable of being used for imaging. The diameter of the aperture of the main objective is a common criterion for comparison among optical systems, such as large telescopes.
The two traditional ...
*
Fresnel lens
A Fresnel lens ( ; ; or ) is a type of composite compact lens developed by the French physicist Augustin-Jean Fresnel (1788–1827) for use in lighthouses. It has been called "the invention that saved a million ships."
The design allows the c ...
*
Lighthouse lens
A lighthouse is a tower, building, or other type of physical structure designed to emit light from a system of lamps and lenses and to serve as a beacon for navigational aid, for maritime pilots at sea or on inland waterways.
Lighthouses mar ...
References
Bibliography
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{{Ancient Greek mathematics
Optical telescopes