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## 透鏡結構

### 製鏡者方程式

${\displaystyle {\frac {1}{f}}=\left({\frac {n}{n_{m}}}-1\right)\left[{\frac {1}{R_{1}}}-{\frac {1}{R_{2}}}+{\frac {(n-1)d}{nR_{1}R_{2}}}\right],}$

${\displaystyle f}$是透鏡的焦距。
${\displaystyle n}$是透鏡材料的折射率
${\displaystyle n_{m}}$是包圍在透鏡材料四周物質的折射率。
${\displaystyle R_{1}}$是透鏡靠近光源這一側表面的曲率半徑。
${\displaystyle R_{2}}$是透鏡遠離這一側表面的曲率半徑。
${\displaystyle d}$是透鏡的厚度（沿著光軸上，透鏡兩個面之間的距離）

#### 薄透鏡方程式

${\displaystyle {\frac {1}{f}}=\left({\frac {n}{n_{m}}}-1\right)\left[{\frac {1}{R_{1}}}-{\frac {1}{R_{2}}}\right].}$

## 成像特点

u>2f f<v<2f 倒立缩小 照相机人眼
u=2f v=2f 倒立等大 等大像法测焦距、影印機
f<u<2f v>2f 倒立放大 幻灯机、投影仪、放映机
u=f v=∞ 不成像 燈塔、探照燈
u<f v>u 正立放大的虚像 放大镜

## 參考資料

1. ^ Pliny the Elder, The Natural History（trans. John Bostock）Book XXXVII, Chap. 10.
2. ^ Pliny the Elder, The Natural History（trans. John Bostock）Book XXXVII, Chap. 16
3. ^ Rashed, R. (1990). "A pioneer in anaclastics: Ibn Sahl on burning mirrors and lenses." Isis, 81, 464–491.
4. ^ 吴毓江，墨子校注，北京：中华书局，1993年，第533页
5. ^ Greivenkamp, p.14; Hecht §6.1

## 外部連結

This article uses material from the Wikipedia article "透镜", which is released under the Creative Commons Attribution-Share-Alike License 3.0. There is a list of all authors in Wikipedia

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