Question

A convex lens of focal length $40cm$ is in contact with a concave lens of focal length $25cm$. The power of the combination is

• A. $-6.5D$
• B. $-6.67D$
• C. $6.5D$
• D. $-1.5D$

Answer 1

The correct option is D

$-1.5D$

Step 1: Given data-

The focal length of the convex lens is $f_1=40cm$ we know the focal length of the convex lens is always positive.

The focal length of the concave lens is $f_2=-20cm$we know the focal length of a concave lens is always negative

Step 2: Evaluate the power of combined lenses-

We know that combined focal length is given by

$\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}$

By substituting values we get

$$\begin{gathered} \Rightarrow \frac{1}{f}=\frac{1}{40}-\frac{1}{25} \\ \Rightarrow \frac{1}{f}=\frac{-40+25}{40\times 25}=-\frac{3}{200}c{m}^{-1}=-1.5m^{-1} \end{gathered}$$

Step 3: Calculate the power of the combination of the lenses-

The power of the lens is given by $P=\frac{1}{f}$ and if the focal length is in meters then the unit of power is dioptre.

Therefore, the power of the combination is $-1.5D$

Hence, the correct option is (d) $-1.5D$.