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Draw a ray diagram to show the formation of an erect image of an object kept in front of a concave mirror. Hence deduce the mirror formula.

Answers (1)

$\Delta ABC$ and $\Delta A'B'C '$ are similar

$\frac{AB}{A'B'}= \frac{BC}{B'C}$ ......(1)

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

$\frac{AB}{A'B'}= \frac{BP}{B'P}$ .......(2)

From equation (1) and (2)

$\frac{BC}{B'C'}= \frac{BP}{B'P}$

Now measuring all distance from P

$\frac{BP}{B'P}=\frac{PC-PB}{PC+PB'}$

$\frac{-u}{v}=\frac{-R(-u)}{-R+(+v)} \Rightarrow \frac{-u}{v}= \frac{-R+u}{-R+v}$

$-u(R+v)= v(-R+u)$

$uR-uv = -Rv+uv$

$uR+vR= 2uv$

Divide throughout by uvR

$\frac{uR}{uvR}+\frac{vR}{uvR}= \frac{2uv}{uvR}$ R= 2f

$\frac{1}{v}+\frac{1}{u}= \frac{2}{R}$

$\frac{1}{v}+\frac{1}{u}= \frac{2}{2f}$

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

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