A convex lens of focal length $50 \mathrm{cm}$ and a concave lens of focal length $100 \mathrm{cm}$ are separated by a distance of $10 \mathrm{cm}$. What is the power of the combination?

The focal length of the combination is

$\frac{1}{\mathrm{F}}=\frac{1}{{\mathrm{f}}_1}+\frac{1}{{\mathrm{f}}_2}-\frac{\mathrm{t}}{{\mathrm{f}}_1{\mathrm{f}}_2}$

where,

$$\begin{gathered} {\mathrm{f}}_1=+50 \mathrm{cm} = 0.5 \mathrm{m}, \\ {\mathrm{f}}_2=-100 \mathrm{cm} = 1 \mathrm{m}, \end{gathered}$$

and $\mathrm{t} = 10 \mathrm{cm} = 0.1 \mathrm{m}$.
Using these values, we get:

$\frac{1}{\mathrm{F}}=\frac{1}{(0.5)}+\frac{1}{(-1)}-\frac{0.1}{(0.5)(-1)} = 1.2 {\mathrm{m}}^{-1}$

Power, $\mathrm{P} = \frac{1}{\mathrm{F}} = 1.2 \mathrm{D}$