Answer
a) $d_{\circ}=14.0cm$
b) $d_{\circ}=8.97cm$
Work Step by Step
(a) We can find the required angular magnification as
$M=\frac{N}{f}$
We plug in the known values to obtain:
$M=\frac{25cm}{14.0cm}$
$M=1.8$
And thus the object distance is:
$d_{\circ}=(\frac{1}{f_1}-\frac{1}{-\infty})^{-1}$
$d_{\circ}=(\frac{1}{14.0cm}-0)^{-1}=14.0cm$
(b) We know that
$M=1+\frac{N}{f}$
$M=1+\frac{25}{14.0}=2.8$
Now the object distance is
$d_{\circ}=(\frac{1}{f_1}-\frac{1}{-N})^{-1}$
$d_{\circ}=(\frac{1}{14.0cm}-\frac{1}{-25.0cm})^{-1}$
$d_{\circ}=8.97cm$
