What is the derivation of lens formula for convex lens

ΔABC is similar to ΔA’B’C

Therefore, [latex]frac{AB}{A’B’}=frac{CB}{CB’}[/latex] (equ.1)

Draw DC = AB

In ΔDCF~ ΔA’B’F

[latex]frac{DC}{A’B’}=frac{CF}{B’F}[/latex] [latex]frac{AB}{A’B’}=frac{CF}{B’F}[/latex] (equ.2)

From equ.1 and equ.2,

[latex]frac{CB}{CB’}=frac{CF}{CB’+CF}[/latex] [latex]frac{+u}{+v}=frac{f}{-v+f}[/latex]

u(-f-v) = fv

Uf – uv = fv

Dividing by u,v,f we get,

[latex]frac{1}{v}-frac{1}{f}=frac{1}{u}[/latex] [latex]frac{1}{f}=frac{1}{v}-frac{1}{u}[/latex]

Therefore, above is the derivation of the lens formula for a convex lens.

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