What is the derivation of 1/f=1/u+1/v

Answers (1)

From \Delta \; A'\; B'\; F and M\; F\; P by similarity criteria.

\frac{A'B;}{MP}=\frac{B'F}{FP} Or \frac{A'B'}{AB}=\frac{B'F}{FP}\; \; \;\; (PM=BA)

Similarly from

 \Delta A'B'P and ABP

    \frac{B'A}{BA}=\frac{B'P}{BP}

    \frac{B'F}{FP}=\frac{B'P}{BP}

    B'F=v+f

    BP=u

   \therefore \frac{v+f}{f}=\frac{v}{u}

    1+\frac{v}{f}=\frac{v}{u}

Dividing throughout by v and applying sign convention

    \frac{1}{v}-\frac{1}{f}=\frac{-1}{u}

    \frac{1}{f}=\frac{1}{v}+\frac{1}{u} 

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