易‧繫辭上

易曰「自天祐之，吉，无不利」。子曰：「祐者，助也。」天之所助者順也，人之所助者信也。履信思乎順，又以尚賢也。是以自天祐之，吉，无不利也。子曰：「書不盡言，言不盡意。」然則聖人之意，其不可見乎？子曰：「聖人立象以盡意，設卦以盡情偽，繫辭以盡其言，變而通之以盡利，鼓之舞之以盡神，乾坤其易之縕邪 ？」乾坤成列，而易立乎其中矣，乾坤毀，則无以見易。易不可見 ，則乾坤或幾乎息矣。是故，形而上者謂之道，形而下者謂之器，化而裁之謂之變，推而行之謂之通，舉而錯之天下之民，謂之事業 。是故，夫象，聖人有以見天下之賾，而擬諸其形容。象其物宜，是故謂之象。聖人有以見天下之動，而觀其會通，以行其典禮，繫辭焉以斷其吉凶，是故謂之爻。極天下之賾者存乎卦，鼓天下之動者存乎辭，化而裁之存乎變，推而行之存乎通，神而明之存乎其人 。默而成之，不言而信，存乎德行。

莊子‧外物

荃者所以在魚，得魚而忘荃；蹄者所以在兔，得兔而忘蹄；言者所以在意，得意而忘言。吾安得夫忘言之人而與之言哉！

 

東晉時陶淵明在《五柳先生傳》中寫到︰

好讀書，不求甚解；毎有會意，便欣然忘食。

是否深知『書不盡言，言不盡意。』？深了『言者所以在意，得意而忘言。』的呢？？單單『不求甚解 』一詞如何解釋往往南轅北轍的哩！有人認為是淺嘗輒止式的不清不楚。也有人以為是虛懷若谷般的自謙之言。直叫人對此『不求甚解 』之詞，來個不求甚解 的了 ！！若問︰既然想『淺嘗輒止』，幹嘛要『好讀書』？假使想自謙『虛懷若谷』，也許會講自己沒讀過幾本書的吧！更何況一句話的意義，需要前言後語通讀，不可隨意斷章取義，否則『每有會意』之『每』意指『每每』？或許與『淺嘗輒止』者矛盾矣？？其實此『每每』者正如《論語》《學而》篇之『學而時習之』者，早曉得輪扁斲輪之故事︰

桓公讀書於堂上，輪扁斲輪於堂下，釋椎鑿而上，問桓公曰：『敢問：公之所讀者，何言邪？』公曰：『聖人之言也。』曰：『聖人在乎？』公曰：『已死矣。』曰：『然則君之所讀者，古人之糟魄已夫！』桓公曰：『寡人讀書，輪人安得議乎！有說則可，無說則死！』輪扁曰：『臣也以臣之事觀之。斲輪，徐則甘而不固，疾則苦而不入，不徐不疾，得之於手而應於心，口不能言，有數存焉於其間。臣不能以喻臣之子，臣之子亦不能受之於臣，是以行年七十而老斲輪。古之人與其不可傳也死矣，然則君之所讀者，古人之糟魄已夫！』

以至於︰

古之學者為己。然而問『學』之『道』貴在能『心有疑』又還『感覺怪』，『去疑除怪』以至於『哈哈大笑』幽默一番，有益於『身心健康』。故

─── 所謂文字，得意忘言，能不能傳，誰知誰了？！ ───

就像金文裡有『』甚字，《說文解字》講：甚，尤安樂也。从甘，从匹耦也。，古文甚。焉知為何字義竟從『安樂』變成『過度』的耶？？！！所以『每每者』今日不解，明日再解；日日解之不解，待時趁機而解。這才謂『不求甚解者』乎！！？？

因此學習者能由自己的學習過程中知道︰從一般原理

前三篇文本中，我們談了一般『光學矩陣』

只要 ，都可借著『自由空間』

化成一個等效之『薄透鏡』

。

因此在『主平面』之參考系裡，分享著同樣的『成像公式』

，具有相同『成像條件』， 參數為

。

甚至可以『串接成像』

的矣！如是就確定了參數 之『聚焦』地位，以及參數 的『影像縮放』性質！！

─── 摘自《光的世界︰矩陣光學六庚》

 

到推導說明具體物件之設計概念與應用想法，尚須下功夫也。

既有上篇範例，也有《光的世界︰【□○閱讀】話眼睛《一》》之系列文本，且題一問，邀請讀者嘗試解讀維基百科放大鏡詞條︰

Magnifying glass

A magnifying glass (called a hand lens in laboratory contexts) is a convex lens that is used to produce a magnified image of an object. The lens is usually mounted in a frame with a handle (see image).

A sheet magnifier consists of many very narrow concentric ring-shaped lenses, such that the combination acts as a single lens but is much thinner. This arrangement is known as a Fresnel lens.

A magnifying glass can also be used to focus light, such as to concentrate the sun’s radiation to create a hot spot at the focus for fire starting.

The magnifying glass is an icon of detective fiction, particularly that of Sherlock Holmes.

Text seen through a magnifying glass

History

The earliest evidence of a magnifying device was a joke in Aristophanes‘s The Clouds from 424 BC, where magnifying lenses to start kindling were sold in a pharmacy, and Pliny the Elder‘s “lens”, a glass globe filled with water, used to cauterize wounds. (Seneca wrote that it could be used to read letters “no matter how small or dim”).^[1] Roger Bacon described the properties of a magnifying glass in 13th-century England. Eyeglasses were developed in 13th-century Italy.^[2]

Magnification

The magnification of a magnifying glass depends upon where it is placed between the user’s eye and the object being viewed, and the total distance between them. The magnifying power is equivalent to angular magnification (this should not be confused with optical power, which is a different quantity). The magnifying power is the ratio of the sizes of the images formed on the user’s retina with and without the lens.^[3] For the “without” case, it is typically assumed that the user would bring the object as close to one eye as possible without it becoming blurry. This point, known as the near point, varies with age. In a young child, it can be as close as 5 cm, while, in an elderly person it may be as far as one or two metres. Magnifiers are typically characterized using a “standard” value of 0.25 m.

The highest magnifying power is obtained by putting the lens very close to one eye and moving the eye and the lens together to obtain the best focus. The object will then typically also be close to the lens. The magnifying power obtained in this condition is MP₀ = (0.25 m)Φ + 1, where Φ is the optical power in dioptres, and the factor of 0.25 m represents the assumed near point (¼ m from the eye). This value of the magnifying power is the one normally used to characterize magnifiers. It is typically denoted “m×”, where m = MP₀. This is sometimes called the total power of the magnifier (again, not to be confused with optical power).

However, magnifiers are not always used as described above because it is more comfortable to put the magnifier close to the object (one focal length away). The eye can then be a larger distance away, and a good image can be obtained very easily; the focus is not very sensitive to the eye’s exact position. The magnifying power in this case is roughly MP = (0.25 m)Φ.

A typical magnifying glass might have a focal length of 25 cm, corresponding to an optical power of 4 dioptres. Such a magnifier would be sold as a “2×” magnifier. In actual use, an observer with “typical” eyes would obtain a magnifying power between 1 and 2, depending on where lens is held.

Diagram of a single lens magnifying glass.

Magnifying glass on an arm lamp

 

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