Answer
a) $d_{\circ}=0.833cm$
b) $d_{\circ}=4.2cm$
Work Step by Step
(a) We know that
$\frac{1}{d_{\circ}}+(-\frac{1}{md_{\circ}})=\frac{1}{f}$
We plug in the known values to obtain:
$\frac{1}{d_{\circ}}(1-\frac{1}{1.5})=\frac{1}{2.5cm}$
This simplifies to:
$d_{\circ}=0.833cm$
(b) We know that
$d_i=-md_{\circ}$
$\implies m=-(-1.5)d_{\circ}=1.5d_{\circ}$
As $\frac{1}{d_{\circ}}+\frac{1}{1.5d_{\circ}}=\frac{1}{2.5cm}$
This simplifies to:
$d_{\circ}=4.2cm$
