# 薄透镜

## 薄透镜成像公式的推导

${\displaystyle {\frac {n2}{L2))+{\frac {n1}{L1))={\frac {N2-N1}{R1))}$

${\displaystyle {\frac {n3}{L3))-{\frac {n2}{L2))={\frac {N3-N2}{-R2))}$

${\displaystyle {\frac {1}{L3))+{\frac {1}{L1))={\frac {N2-1}{R1))+{\frac {1-N2}{R2))}$
${\displaystyle {\frac {1}{L3))+{\frac {1}{L1))=(N2-1)({\frac {1}{R1))-{\frac {1}{R2)))}$

${\displaystyle {1 \over D}+{1 \over d'}=(N-1)*({\frac {1}{R1))-{\frac {1}{R2)))}$

${\displaystyle {1 \over d}=(N-1)*({\frac {1}{R1))-{\frac {1}{R2)))}$

${\displaystyle {1 \over f}=(N-1)*({\frac {1}{R1))-{\frac {1}{R2)))}$
${\displaystyle {1 \over D}+{1 \over d}={1 \over f))$

${\displaystyle f}$称为薄透镜焦距。其中N是薄透镜的材料折射率，R1,R2是球面的半径，半径的方向和光轴相同为正号，反之为负号。

f >0的透镜称为凸透镜，f <0的透镜称为凹透镜。

${\displaystyle \phi ={1 \over f))$

## 高斯公式

${\displaystyle {1 \over D}+{1 \over d}={1 \over f))$ （物距（D）和像距（d）），通分后可得

${\displaystyle D*d=f*(D+d)}$

${\displaystyle D*d-f*D-f*d=0}$

${\displaystyle D*d-f*D-f*d+f^{2}=f^{2))$

${\displaystyle (D-f)*(d-f)=f^{2))$

## 倍率

${\displaystyle M={\frac {h}{H))={\frac {d}{D))}$

${\displaystyle d=f*(M+1)}$

${\displaystyle D={\frac {M+1}{M))f}$

${\displaystyle D=d=2f}$

## 薄透镜的弯曲术

${\displaystyle {1 \over f}=(N-1)*({\frac {1}{R1))-{\frac {1}{R2)))}$

${\displaystyle {\frac {1}{f))=(N-1)*(c1-c2)=(N-1)*c}$

${\displaystyle {\frac {1}{f))=(N-1)*(c1-c2)=(N-1)*((c1+k)-(c2+k))=(N-1)*c}$

## 两个薄透镜的组合

${\displaystyle p=p_{1}+p_{2}-d*p_{1}*p_{2))$

${\displaystyle p=p_{1}+p_{2))$

## 参考文献

1. ^ A.E.Conrady Applied Optics and Optical Design Section 23 Simple Lens, p60-62，Dover
2. ^ Dennis Taylor p9-10