关于光学一个公式的推导
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关于光学一个公式的推导
1/u+1/v=1/f
怎么推的,
1/u+1/v=1/f
怎么推的,
![关于光学一个公式的推导](/uploads/image/z/9994656-48-6.jpg?t=%E5%85%B3%E4%BA%8E%E5%85%89%E5%AD%A6%E4%B8%80%E4%B8%AA%E5%85%AC%E5%BC%8F%E7%9A%84%E6%8E%A8%E5%AF%BC)
如图,画两条特殊光线.
因为ΔADA'∽ΔOF’A',所OA'/AA'=OF'/AD=f/u (1)
又因为ΔOA'B'∽ΔAOD,所以OA'/OA=OB'/AD=v/u
即 OA'/AA'=OA'/(OA+OA')=v/(v+u) (2)
(1)(2)联立,化简,得1/f=1/u+1/v
![](http://img.wesiedu.com/upload/8/5f/85f037bd571a0a8d38a49483c4f4fed0.jpg)
因为ΔADA'∽ΔOF’A',所OA'/AA'=OF'/AD=f/u (1)
又因为ΔOA'B'∽ΔAOD,所以OA'/OA=OB'/AD=v/u
即 OA'/AA'=OA'/(OA+OA')=v/(v+u) (2)
(1)(2)联立,化简,得1/f=1/u+1/v
![](http://img.wesiedu.com/upload/8/5f/85f037bd571a0a8d38a49483c4f4fed0.jpg)