Answer
$m = -2.5$
Work Step by Step
When $p = 5.0~cm$, we can see that $m = 2$
We can find $i$:
$m = -\frac{i}{p}$
$i = -mp$
$i = -(2)(5.0~cm)$
$i = -10~cm$
We can find $r$:
$\frac{1}{p}+\frac{1}{i} = \frac{2}{r}$
$\frac{1}{5.0~cm}+\frac{1}{-10~cm} = \frac{2}{r}$
$\frac{2}{r} = \frac{1}{10~cm}$
$r = 20~cm$
We can find $i$ when $p = 14.0~cm$:
$\frac{1}{p}+\frac{1}{i} = \frac{2}{r}$
$\frac{1}{i} = \frac{2}{r}-\frac{1}{p}$
$\frac{1}{i} = \frac{2}{20~cm}-\frac{1}{14.0~cm}$
$\frac{1}{i} = \frac{1}{35.0~cm}$
$i = 35.0~cm$
We can find $m$ when $p = 14.0~cm$:
$m = -\frac{i}{p}$
$m = -\frac{35.0~cm}{14.0~cm}$
$m = -2.5$
