Answer to Question #300405 in Optics for sara

Question

A 1.6 m tall girl stands 3.2 m from a convex mirror . What is the focal length of the mirror if her image appears to be 0.28 m tall? 

Answer 1

$m=\frac{h_i}{h_o}=-\frac{d_i}{d_o}$

$d_i=-\frac{h_i d_o}{h_o}$

$=-\frac{(0.28m)(3.2m)}{1.6m} =-0.56m$

$\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}$

$f=\frac{d_o d_i}{d_o+d_i}$

$=\frac{(3.2m)(-0.56m)}{3.2m+(-0.56m)}=-0.68m$