樹莓派、樹莓派之學習、樹莓派之教育

光的世界︰【□○閱讀】樹莓派近攝鏡‧下‧答之合

放大鏡之歷史久遠矣︰

放大透鏡的歷史可追溯至古埃及，約西元前五世紀，以埃及的象形文字表示「一片玻璃透鏡」。最早的文字記載則可追溯到古羅馬，約公元前一世紀，羅馬皇帝尼祿的導師塞內卡寫道「無論多小或模糊的文字，透過球體或注滿水的玻璃壺就會放大」。[1]亦有一說尼錄皇帝曾以一個祖母綠寶石當做凸透鏡來觀賞鬥士比賽。[2]

早於千多年前，人們已把透明水晶或寶石磨成「透鏡」，這些透鏡可放大影像。

 

一位喜歡觀察自然萬物的人，也許早已見過它多變的形貌也︰

Water Droplet as a Simple Magnifier

 A water droplet can act as a simple magnifier and magnify the object behind it. Water tends to form spherical droplets under the influence of surface tension. When attached to an object like these examples, the spherical shape is distorted, but still capable of forming an image. Above the droplets are on tiny emerging pine cones. At left the droplet forms a partial image of the flower that is out of focus behind it.

 

所謂明視距離，也稱作近點，就是眼睛能聚焦清晰成像的最短距離 ，成年人通常大約是 25 公分。因此在觀察小東西時。需要放大鏡才能看的更清楚物件之紋理。若將放大鏡緊貼眼睛，就彷彿相機加裝近攝鏡一樣，因此可以更近的距離觀物︰

\frac{1}{X_{=25cm}} + \frac{1}{X_{retina}} = \frac{1}{f_{eye}} \ (1)

\frac{1}{X_{min}} + \frac{1}{X_{retina}} = \frac{1}{f_{eq.}} \ (2)

而且 \frac{1}{f_{eq.}} = \frac{1}{f_{eye}} + \frac{1}{f_{mag}} 。從 (2) -(1) ，解之得

X_{min} = \frac{X_{=25cm}}{D_{mag} X_{=25cm} + 1}

\therefore \frac{1}{X_{min}} = \frac{1}{f_{mag}} + \frac{1}{25} 。因為

M_{X_{min} \cdot X_{min} = M_X_{=25cm} \cdot X_{=25cm} = X_{retina} ，所以

M_{X_{min} = \frac{X_{retina}}{X_{min}} = M_X_{=25cm} \cdot \frac{X_{=25cm}}{X_{min}} = M_X_{=25cm} (D_{mag} X_{=25cm} + 1)

\therefore \frac{M_{X_{min} }}{M_X_{=25cm}} = \frac{25}{f_{mag}} + 1

假使單從放大鏡成像來講，

\frac{1}{d_o} + \frac{1}{d_i} = \frac{1}{f_{mag}}

前焦距內之物 d_o < f_{mag}越靠近焦點 {d_o}^- \to f_{mag}，虛像將趨近於與物同邊之無窮遠處 d_i \to - \infty 。若以接續成像來講，此時眼睛與放大鏡中間的距離，對比下大可以忽略不計。因此從相對角放大率觀之，

M_{{d_o}^- \to f_{mag} = \frac{25}{f_{mag}}

的了。不過還是多讀讀幾家文本，加深印象與理解的好耶☆

Simple Magnifier

 The simple magnifier achieves angular magnification by permitting the placement of the object closer to the eye than the eye could normally focus. The standard close focus distance is taken as 25 cm, and the angular magnification is given by the relationships below.

This precision magnifier performs the role of a simple magnifier, but has multiple elements to overcome aberrations and give a sharper image. Lens combinations are used to make high quality magnifiers for use as eyepieces.

 

光學 標題:放大鏡的原理
1:黃福坤 (研究所)張貼:2006-10-22 12:39:58:

上圖顯示眼睛直接觀看蜜蜂時在視網膜上呈現的大小,圖中 dn通常是明視距離也就是正常狀況為25cm. 視角= y0/dn下圖則顯示使用放大鏡後的效果,視角=yi/L

比較兩圖可以知道 眼睛看物體的視角變大了！
兩者視角的放大比率就是 放大鏡的放大率（注意和一般透鏡放大率的定義M=-si/so=yi/yo不同） 放大鏡的放大率=(yi/L)/(yo/dn)=-si*dn/(so*L)使用放大鏡時 物體通常非常接近焦距（si->L, so->f) 所以放大鏡的（角）放大倍率= dn/f 只和透鏡的焦距有關！