レンズの公式
A : B = F : ( B − F ) A ( B − F ) = B F A B − A F = B F B F + A F = A B {\displaystyle {\begin{array}{lcl}A:B&=&F:(B-F)\\A(B-F)&=&BF\\AB-AF&=&BF\\BF+AF&=&AB\end{array}}}
となり、これを ( A B F ) {\displaystyle (ABF)} で割ると
B F A B F + A F A B F = A B A B F ∴ 1 A + 1 B = 1 F {\displaystyle {\begin{array}{lcl}{\frac {BF}{ABF}}+{\frac {AF}{ABF}}&=&{\frac {AB}{ABF}}\\\therefore {\frac {1}{A}}+{\frac {1}{B}}&=&{\frac {1}{F}}\end{array}}}
(証明終わり)