# Draw a ray diagram to show formation of a virtual image of an object by convex lens. Using this diagram, obtain the expression for the lens formula.

$\Delta A'B'P$ and $\Delta ABP$ are similar

$\frac{AB}{A'B'}= \frac{BP}{B'P}= \frac{-u}{-v}$              ...........(1)

$\Delta A'B'P$ and $\Delta MPF$ are similar

$\frac{MP}{A'B'}= \frac{PF}{B'P}= \frac{f}{B'P+PF}= \frac{f}{-v+f}$

From the diagram, AB = MP

$\therefore \frac{AB}{A'B'}= \frac{f}{-v+f}$

$\frac{-u}{-v}= \frac{f}{-v+f}\Rightarrow \frac{u}{v}= \frac{f}{-v+f}$

$u(-v+f)=fv$

$uf-uv=fv$

Divide throughout by uvf

$\frac{uf}{uvf}-\frac{uv}{uvf}=\frac{fv}{uvf}$

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

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

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