Question

Explain mirror formula $\frac{1}{u}+\frac{1}{v}=\frac{1}{f}$.

Answer 1

$\frac{AB}{A^{\prime }{B}^{\prime }}=\frac{AC}{A^{\prime }{C}^{\prime }}$

$\frac{BP}{A^{\prime }{B}^{\prime }}=\frac{PF}{A^{\prime }{F}^{\prime }}$

$\therefore \frac{AB}{A^{\prime }{B}^{\prime }}=\frac{PF}{A^{\prime }F}$

$PF=-f$ $AP=-u$

$A^{\prime }P=-v$

$\frac{(-2f)-(-v)}{-u-(-2f)}=\frac{-v-(-f)}{-f}$

$\therefore uv=fv+uf$

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

$\frac{n_2}{n_1}=\frac{A^{\prime }{B}^{\prime }}{AB}$

$=\frac{A^{\prime }P}{AP}$

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