Answer
$55cm$
Work Step by Step
First, we can use the given values from the table in the lens makers equation to find the focal point.
$\frac{1}{f}=(n-1)(\frac{1}{r_1} - \frac{1}{r_2})$
Solving for $f$, we obtain:
$f=((n-1)(\frac{1}{r_1} - \frac{1}{r_2}))^{-1}$
$f=((1.55-1)(\frac{1}{30cm} - \frac{1}{-42cm}))^{-1}$
$f=+31.8cm$
Now we can use equation 34-9 to find the image distance, $i$:
$\frac{1}{p}+\frac{1}{i}=\frac{1}{f}$
Solving for $i$, we have:
$i=(\frac{1}{f}-\frac{1}{p})^{-1}$
$i=(\frac{1}{31.8cm}-\frac{1}{75cm})^{-1}$
$i=+55cm$