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)
S safeer

\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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