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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

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

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

Posted by

Safeer PP

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