Answer
$24.2cm$
Work Step by Step
The required height of the image can be determined as follows:
$d_{i1}=\frac{(f_1)(d_{\circ})}{d_{\circ}-f_1}$
$\implies d_{i1=\frac{(20.5cm)(30.0cm)}{30.0cm-20.5cm}}$
$\implies d_{i1}=64.73cm$
and the object distance for the second lens is $d_{\circ 2}=30.0cm-64.73cm=-34.73cm$
Now the image distance for the second lens is given as
$d_{i2}=\frac{f_2 d_{\circ 2}}{d_{\circ 2}-f_2}$
We plug in the known values to obtain:
$d_{i2}=\frac{(-42.5cm)(-34.73cm)}{-34.73cm+42.5cm}$
$\implies d_{i2}=190cm$
The height of the image is given as
$h_i=(-\frac{-d_{i1}}{d_{\circ}})(-\frac{d_{i2}}{d_{\circ 2}})h_{\circ}$
We plug in the known values to obtain:
$h_i=(\frac{-64.73cm}{30.0cm})(\frac{190cm}{-34.73cm})(2.05cm)$
$\implies h_i=-24.2cm$
