Explanation

(a) $\frac{1}{f_{a}} = (\mu - 1)(\frac{1}{R_{1}} - \frac{1}{R_{2}})$
$= (1.5 - 1)\left( \frac{1}{R_{1}} - \frac{1}{R_{2}} \right)\ \ \ \ \ \ \ \ \ldots\ldots\ldots\ldots..(i)$
$and\frac{1}{f_{m}} = \frac{\mu_{g} - \mu_{m}}{\mu_{m}}(\frac{1}{R_{1}} - \frac{1}{R_{2}})$
$\frac{1}{f_{m}} = \left( \frac{1.5}{1.6} - 1 \right)\left( \frac{1}{R_{1}} - \frac{1}{R_{2}} \right)\ \ \ \ \ldots\ldots\ldots..(ii)$
Thus,
$\frac{f_{m}}{f_{a}} = \frac{(1.5 - 1)}{\left( \frac{1.5}{1.6} - 1 \right)} = - 8$
$f_{m} = \ - 8 \times fₐ$
$= - 8 \times \frac{- 1}{5}\ \ \ \ \ \ \ \ \ \left( \because f_{a} = \frac{1}{p} = - \frac{1}{5}m \right)$
$= 1.6\ m$
$\therefore P_{m} = \frac{\mu}{f_{m}}$
$= \frac{1.6}{1.6} = 1D$