Question

What is the focal length of a convex lens of focal length $30\mathrm{cm}$ in contact with a concave lens of focal length $20\mathrm{cm}$ ? Is the system a converging or a diverging lens? Ignore the thickness of the lenses.

Answer 1

Step 1: Given information

The focal length of the convex lens is ${\mathrm{f}}_1=30\mathrm{cm}$.

The focal length of the concave lens is ${\mathrm{f}}_2=-20\mathrm{cm}$

Step 2: To find

The focal length of a convex lens

Step 3: Finding the focal length

We know the formula,

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

By substituting the values,

$$\begin{gathered} \Rightarrow \frac{1}{\mathrm{f}}=\frac{1}{30}-\frac{1}{20} \\ \Rightarrow =\frac{2-3}{60} \\ \Rightarrow =-\frac{1}{60} \\ \Rightarrow \mathrm{f}=-60\mathrm{cm} \end{gathered}$$

Hence, the combined focal length of the lenses is $60\mathrm{cm}$ and, the negative sign implies that its lens system is a diverging lens.