Answer
(a) farther away
(b) $2.8cm$
Work Step by Step
(a) We know that $m=\frac{f}{f-d_{\circ}}$. This equation shows that the object is placed at a distance of less than $f$ to get the given positive magnification (m=3). Thus, to increase the magnification to $4.0$, we should move the object away from the lens.
(b) We know that
$d_{\circ}=f(1-\frac{1}{m})$
We plug in the known values to obtain:
$d_{\circ}=34(1-\frac{1}{3})cm=22.67cm$
If we increase the magnification to $4.0$, then the object distance becomes
$d_{\circ}=f(1-\frac{1}{m})$
We plug in the known values to obtain:
$d_{\circ}=34(1-\frac{1}{4})cm=25.5cm$
Thus the change in the object distance is $25.5cm-22.67cm=2.8cm$
