若問 $m_o = - \frac{L}{f_o}$ 和 $M_e = \frac{25}{f_e}$ 從何來？

Compound Microscope

A compound microscope uses a very short focal length objective lens to form a greatly enlarged image. This image is then viewed with a short focal length eyepiece used as a simple magnifier. The image should be formed at infinity to minimize eyestrain.

The general assumption is that the length of the tube L is large compared to either f_o or f_e so that the following relationships hold.

In a working microscope, the length L in the sketch above is much longer than either of the lens focal lengths f_o and f_e.

為何置物 $f_o$ 與 $2 f_o$ 之間耶？？

2:黃福坤(研究所)張貼:2006-10-22 13:02:58:

而顯微鏡則是將物體放置於透鏡焦距到兩倍焦距之間,然後將所形成的像再度透過第二個透鏡以放大鏡的方式放大如下圖

$M_e = \frac{25}{f_e}$ 由來已說過︰

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.