Catoptrics

Light path of a Newtonian (catoptric) telescope

Catoptrics (from Greek: κατοπτρικός katoptrikós, "specular",^[1] from Greek: κάτοπτρον katoptron "mirror"^[2]) deals with the phenomena of reflected light and image-forming optical systems using mirrors. A catoptric system is also called a catopter (catoptre).

Ancient texts

Catoptrics is the title of two texts from ancient Greece:

• The Pseudo-Euclidean Catoptrics. This book is attributed to Euclid,^[3] although the contents are a mixture of work dating from Euclid's time together with work which dates to the Roman period.^[4] It has been argued that the book may have been compiled by the 4th century mathematician Theon of Alexandria.^[4] 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, this work concerns the practical application of mirrors for visual effects. In the Middle Ages, this work was falsely ascribed to Ptolemy. It only survives in a Latin translation.^[5]

The Latin translation of Alhazen's (Ibn al-Haytham) main work, Book of Optics (Kitab al-Manazir),^[6] exerted a great influence on Western science: for example, on the work of Roger Bacon, who cites him by name.^[7] His research in catoptrics (the study of optical systems using mirrors) centred on spherical and parabolic mirrors and spherical aberration. He made the observation that the ratio between the angle of incidence and refraction does not remain constant, and investigated the magnifying power of a lens. His work on catoptrics also contains the problem known as "Alhazen's problem".^[8] Alhazen's work influenced Averroes' writings on optics,^[9] 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 [Ibn al-Haytham's] Optics).^[10]

Catoptric telescopes

The first practical catoptric telescope (the "Newtonian reflector") was built by Isaac Newton as a solution to the problem of chromatic aberration exhibited in telescopes using lenses as objectives (dioptric telescopes).

See also

• Dioptrics
• Catadioptrics
• Optical telescope
• List of telescope types
• Image-forming optical system
• Fresnel lens
• Lighthouse lens

References

1. A Concise Dictionary of the English and Modern Greek Languages by Antonius Nicholas Jannaris, 1895 J. Murray
2. "Henry George Liddell, Robert Scott, An Intermediate Greek-English Lexicon, κάτοπτρον". Retrieved 2015-03-13.
3. Reading Euclid by J. B. Calvert, 2000 Duke U. accessed 23 October 2007
4. O'Connor, John J.; Robertson, Edmund F., "Catoptrics", MacTutor History of Mathematics archive, University of St Andrews., accessed 31 January 2013
5. A. Mark Smith, (1999), Ptolemy and the Foundations of Ancient Mathematical Optics, pages 16-17. American Philosophical Society. ISBN 0871698935
6. Grant 1974 p.392 notes the Book of Optics has also been denoted as Opticae Thesaurus Alhazen Arabis, as De Aspectibus, and also as Perspectiva
7. (Lindberg 1996, p. 11), passim
8. (Dr. Al Deek 2004)
9. (Topdemir 2007a, p. 77)
10. (El-Bizri 2005a)
    (El-Bizri 2005b)

• Dr. Al Deek, Mahmoud (2004), "Ibn Al-Haitham: Master of Optics, Mathematics, Physics and Medicine", Al Shindagah (November–December 2004)