Question

An object 1.00cm high is placed 18.0cm from a converging lens forms a real image 2.00cm high. Calculate the focal length of the lens

Answer 1

Given:

$d_o=18.0\:\rm cm$

$h_o=1.00\:\rm cm$

$h_i=-2.00\:\rm cm$

The magnification of thin lenth

$$m=\frac{h_i}{h_o}=-\frac{d_i}{d_0}$$

Hence,

$$d_i=-d_o\frac{h_i}{h_o}=-18.0\times\frac{-2.00}{1.00}=36.0\:\rm cm$$

The thin lens equation says

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

Finally,

$$f=\frac{d_od_i}{d_o+d_i}=\frac{18.0*36.0}{18.0+36.0}=12.0\;\rm cm$$