儘管為文主旨是想介紹『矩陣光學』實務應用，如果假設讀者已知 □ ○，這樣只需列出

Table of ray transfer matrices

for simple optical components

Element	Matrix	Remarks
Propagation in free space or in a medium of constant refractive index		d = distance
Refraction at a flat interface		n1 = initial refractive index n2 = final refractive index.
Refraction at a curved interface		R = radius of curvature, R > 0 for convex (centre of curvature after interface) n1 = initial refractive index n2 = final refractive index.
Reflection from a flat mirror		Only valid for mirrors perpendicular to the ray.
Reflection from a curved mirror		effective radius of curvature in tangential plane (horizontal direction)   effective radius of curvature in the sagittal plane (vertical direction) R = radius of curvature, R > 0 for concave, valid in the paraxial approximation is the mirror angle of incidence in the horizontal plane.
Thin lens		f = focal length of lens where f > 0 for convex/positive (converging) lens.Only valid if the focal length is much greater than the thickness of the lens.
Thick lens		n1 = refractive index outside of the lens. n2 = refractive index of the lens itself (inside the lens). R1 = Radius of curvature of First surface. R2 = Radius of curvature of Second surface. t = center thickness of lens.
Single right angle prism		k = (cos  /cos ϕ  ) is the beam expansion factor, where  is the angle of incidence,  is the angle of refraction, d = prism path length, n = refractive index of the prism material. This matrix applies for orthogonal beam exit.

 

就好。但思『事理不二』，要是『理』都不清，『事』能明乎？？那又何必曾講『勸學篇』也！！

訊︰☿ 把酒飛斝是同道，欲法荀子《勸學篇》趁年少︰

君子曰：學不可以已。青，取之於藍而青於藍；冰，水為之而寒於水。〈以喻學則才過其本性也。〉木直中繩，輮以為輪，其曲中規，雖有槁暴，不復挺者，輮使之然也。〈輮，屈。槁，枯。曓，乾。挻，宜也。《晏子春秋》作「不復贏也」。〉故木受繩則直，金就礪則利，君子博學而日參省乎己，則知明而行無過矣。〈參，三也。曾子曰︰「日三省吾身。」知，讀爲智。行，下孟反。〉故不登高山，不知天之高也；不臨深谿，不知地之厚也；不聞先王之遺言，不知學問之大也。〈大，謂有益於人。〉干、越、夷、貉之子，生而同聲，長而異俗，教使之然也。〈干、越，猶言吳、越。《呂氏春秋》「荊有次非得寶劍於干、越」，高誘曰︰「吳邑也。」貉，東北夷。同聲，謂啼聲同。貉，莫革反。〉《詩》曰：「嗟爾君子，無恆安息。靖共爾位，好是正直。神之聽之，介爾景福。」〈《詩》，《小雅‧小明》之篇。靖，謀。介，助。景，大也。無恆安息，戒之不使懷安也。言能謀恭其位，好正宜之道，則神聽而助之福，引此詩以喻勤學也。〉神莫大於化道，福莫長於無禍。〈爲學則自化道，故神莫大焉。修身則自無禍，故福莫長焉。〉吾嘗終日而思矣，不如須臾之所學也，吾嘗跂而望矣，不如登高之博見也 。〈跂，舉足也。〉登高而招，臂非加長也，而見者遠；順風而呼，聲非加疾也，而聞者彰。假輿馬者，非利足也，而致千里；假舟楫者，非能水也，而絕江河。〈能，善。絶，過。〉君子生非異也，善假於物也。〈皆以喻修身在假於學。生非異，言與衆人同也。〉南方有鳥焉，名曰蒙鳩，以羽為巢而編之以髮，繫之葦苕，風至苕折，卵破子死。巢非不完也 ，所繫者然也。〈蒙 鳩，鷦鷯也。苕，葦之秀也，今巧婦鳥之巢至精密，多繫於葦竹之上是也。「蒙」當爲「蔑」。《方言》雲︰「鷦鷯，關而西謂之桑飛，或謂之蔑雀。」或曰︰一名 蒙鳩，亦以其愚也。言人不知學問，其所置身亦猶繫葦之危也。《說苑》︰「客謂孟嘗君曰︰『鷦鷯巢於葦苕，箸之髮毛，可謂完堅矣，大風至則苕折卵破子死者何 也？其所託者然也。』〉西方有木焉，名曰射干，莖長四寸，生於高山之上，而臨百仞之淵，木莖非能長也，所立者然也 。〈《本草》藥名有射干，一名烏扇。陶弘景雲︰「花白莖長，如射人之執竿。」又引阮公詩云「射干臨層城」，是生於高處也。據《本草》在《草部》中，又生南陽川穀，此雲「西方有木」，未詳。或曰︰「長四寸」卽是草，雲木，誤也。蓋生南陽，亦生西方也。射音夜。〉蓬生麻中，不扶而直。蘭槐之根是爲芷。其漸之滫，君子不近，庶人不服，其質非不美也，所漸者然也。〈蘭槐，香草，其根是爲芷也。《本草》︰「白芷一名白茝。」陶弘景雲︰「卽《離騷》所謂蘭茝也。」葢苗名蘭茝，根名芷也。弱槐當是蘭茝別名，故云「蘭槐之根是爲芷」也。漸，漬也，染也。滫，溺也。言雖香草，浸漬於溺中，則可惡也。漸，子廉反。滫，思酒反。〉故君子居必擇鄉，遊必就士，所以防邪僻而近中正也。物類之起，必有所始。榮辱之來，必象其德。肉腐出蟲，魚枯生蠹。怠慢忘身，禍災乃作。強自取柱，柔自取束。〈凡物強則以爲柱而任勞，柔則見束而約急，皆其自取也。〉邪穢在身，怨之所構。〈構，結也。言亦所自取。〉施薪若一，火就燥也；〈布薪於地，均若一，火就燥而焚之矣。〉平地若一，水就溼也。草木疇生，禽獸羣焉，物各從其類也。〈疇與儔同，類也。〉是故質的張而弓矢至焉，林木茂而斧斤至焉，〈所謂召禍也。質，射矦。的，正鵠也。〉樹成蔭而衆鳥息焉，醯酸而蜹聚焉。〈喻有德則慕之者衆。〉故言有召禍也，行有招辱也，君子慎其所立乎！〈禍福如此，不可不慎所立。所立，卽謂學也。〉

積土成山，風雨興焉；積水成淵，蛟龍生焉；積善成德，而神明自得，聖心備焉。〈神明自得，謂自通於神明。〉故不積蹞步，無以致千里；〈半步曰蹞。蹞與跬同。〉不積小流，無以成江海。騏驥一躍，不能十步；駑馬十駕，〈言駑馬十度引車，則亦及騏驥之一躍。據下雲「駑馬十駕，則亦及之」，此亦當同，疑脫一句。〉功在不舍。鍥而舍之，朽木不折；鍥而不舍 ，金石可鏤。〈言立功在於不舍。舍與捨同。鍥，刻也，苦結反。《春秋傳》曰「陽虎借邑人之車，鍥其軸」也。〉螾無爪牙之利，筋骨之強，上食埃土，下飲黃泉，用心一也。〈螾與蚓同，蚯蚓也。〉蟹八跪而二螯，非虵蟺之穴無可寄託者，用心躁也。〈跪，足也。《韓子》以刖足爲刖跪。螫，蟹首上如鉞者。許叔重《說文》雲「蟹六足二螫」也。〉是故無冥冥之志者無昭昭之明 ，無惛惛之事者無赫赫之功。〈冥冥、惛惛，皆專默精誠之謂也。〉行衢道者不至，事兩君者不容。〈《爾雅》雲︰「四達謂之衢。」孫炎雲︰「衢，交道四出也。」或曰︰衢道，兩道也。不至，不能有所至。下篇有「楊朱哭衢塗」。今秦俗猶以兩爲衢，古之遺言歟？〉目不能兩視而明，耳不能兩聽而聰。螣蛇無足而飛，〈《爾雅》云：「螣，螣蛇。」郭璞雲「龍類，能興雲霧而遊其中」也。〉梧鼠五技而窮。〈「梧鼠」當爲「鼫鼠」，蓋本誤爲「鼯」字，傳寫又誤爲「梧」耳。技，才能也。言技能雖多而不能如螣蛇專一，故窮。五技，謂能飛不能上屋，能緣不能窮木，能游不能渡谷，能穴不能掩身，能走不能先人。〉《詩》曰 ：「屍鳩在桑，其子七兮。淑人君子，其儀一兮。其儀一兮，心如結兮。」故君子結於一也。〈《詩》，《曹風‧屍鳩》之篇。毛雲︰「屍鳩，鴶鞠也。屍鳩之養七子，旦從上而下，暮從下而上，平均如一。善人君子，其執義亦當如屍鳩之一。執義一則用心堅固。」故曰「心如結」也。

……… 摘自《M♪o 之學習筆記本《編者跋》》

 

豈非對好學者太失禮耶？？！！

聽聞楊百翰大學多年來開設光學教育課程︰

 

幸得 Justin Peatross 與 Michael Ware 先生們之慷慨︰

 

可以省憂少勞矣！！！故此還請讀者先讀

Optics Textbook

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之『第九章』

 

踏上旅程吧！！？？