A lens has a power of $-4D$. What is the nature and focal length of the lens?

Step 1: Given data

The power of the lens is $P=-4D$.

Step 2: Finding the nature of the lens.

As the power of the lens is negative, the lens used is concave.

Step 3: Finding the focal length of the lens.

According to the power of lens formula,

$P=\frac{1}{f}$

where $f$ is the focal length of the lens in meters.

Substituting the known values,

$$\begin{gathered} -4D=\frac{1}{f} \\ -4m^{-1}=\frac{1}{f} \\ -4=\frac{1}{f} \\ f=-\frac{1}{4} \\ f=-0.25m \\ f=-25cm \end{gathered}$$

Thus, the focal length of the lens is $-25cm$.