因為牛頓知道稜鏡能將白光
一個將光線色散的三稜鏡
分解成彩虹。無怪乎，他會應用
反射光學
反射光學是使用鏡子反射光線和成像的光學系統。開始於希臘的κατοπτρικός (鏡面)[1]。.
反射光學 (Catoptrics)這本書被認為是歐基里德的著作[2]，含蓋著鏡面的數學理論，特別是平面鏡和球面凹鏡城象的數學理論。
第一個實用的反射光學望遠鏡 (“牛頓望遠鏡“) 是艾薩克·牛頓為解決使用透鏡作為物鏡 (屈光學望遠鏡) 的色差而製造的。
牛頓 (反射光學) 望遠鏡的光路圖。
Catoptrics
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]
消除色差，製作望遠鏡哩。現在鏡子依舊常在成像系統︰
Mirrors in Imaging
Mirrors are used widely in optical instruments for gathering light and forming images since they work over a wider wavelength range and do not have the problems of dispersion which are associated with lenses and other refracting elements.
Mirror Instruments
Mirrors are widely used in telescopes and telephoto lenses. They have the advantage of operating over a wider range of wavelengths, from infrared to ultraviolet and above. They avoid the chromatic aberration arising from dispersion in lenses, but are subject to other aberrations. Instruments which use only mirrors to form images are called catoptric systems, while those which use both lenses and mirrors are called catadioptric systems (dioptric systems being those with lenses only).
展露頭角。由於反射是如此普通的現象，因此古代早有人論及
Alhazen’s problem
The medieval mathematician Ibn al-Haytham (Alhazen) solved an important problem known as Alhazen’s problem in his work on catoptrics in Book V of the Book of Optics . The problem was first formulated by Ptolemy in 150 AD.[1]
Geometric formulation
The problem comprises drawing lines from two points in a circle meeting at a third point on its circumference and making equal angles with the normal at that point. This is equivalent to finding the point on the edge of a circular billiard table at which a cue ball at a given point must be aimed in order to carom off the edge of the table and hit another ball at a second given point. Thus, its main application in optics is to solve the problem, “Given a light source and a spherical mirror, find the point on the mirror where the light will be reflected to the eye of an observer.” This leads to an equation of the fourth degree.[2][3][1]
Sums of powers
Ibn al-Haytham eventually derived a formula for the sum of fourth powers, where previously only the formulas for the sums of squares and cubes had been stated. His method can be readily generalized to find the formula for the sum of any integral powers, although he did not himself do this (perhaps because he only needed the fourth power to calculate the volume of the paraboloid he was interested in). He used his result on sums of integral powers to perform what would now be called an integration, where the formulas for the sums of integral squares and fourth powers allowed him to calculate the volume of a paraboloid.[4]
Influence
Ibn al-Haytham solved the problem using conic sections and a geometric proof, but later mathematicians such as Christiaan Huygens, James Gregory, Guillaume de l’Hôpital, Isaac Barrow, and many others, attempted to find an algebraic solution to the problem, using various methods, including analytic methods of geometry and derivation by complex numbers.[5] An algebraic solution to the problem was finally found in 1997 by the Oxford mathematician Peter M. Neumann.[6] Recently, Mitsubishi Electric Research Labs researchers solved the extension of Alhazen’s problem to general rotationally symmetric quadric mirrors including hyperbolic, parabolic and elliptical mirrors.[7] They showed that the mirror reflection point can be computed by solving an eighth degree equation in the most general case. If the camera (eye) is placed on the axis of the mirror, the degree of the equation reduces to six.[8] Alhazen’s problem can also be extended to multiple refractions from a spherical ball. Given a light source and a spherical ball of certain refractive index, the closest point on the spherical ball where the light is refracted to the eye of the observer can be obtained by solving a tenth degree equation.[8]
餘波蕩漾至今？？