Question

Express the power (with sign) of a concave lens of focal length $20cm$.

Answer 1

Hint
The reciprocal of the focal length of the lens can be defined as the power of the lens. It is measured in Diopters (D). In this problem, we can simply substitute the focal length in the power formula to obtain the power of the lens.
Power of the lens (P) = $\dfrac{1}{f}$
Where f is the focal length of the lens in meters

Complete step by step answer
It is given that the lens is concave. Concave lenses have a negative focal length. So, the focal length of the lens will be
Focal length of lens (f) = $ - 20cm = - 0.2m$ [ $1m = 100cm$ ]
We know the formula
Power of the lens (P) = $\dfrac{1}{f}$
By substituting the value of the focal length in the above formula, we get
$ \Rightarrow P = \dfrac{1}{{ - 0.2}}$
$ \Rightarrow P = - 5D$
The power of the lens (P) is $ - 5D$.

Additional Information
- Concave lenses are also known as diverging lenses as the lens diverges the light rays away from the axis
- The focal length is inversely proportional to the power of the lens. So a lens having a shorter focal length will have more power than a lens having a larger focal length.
- Convex (Converging) lenses have positive focal lengths, so the power of the lens will also be positive
- Concave (Diverging) lenses have negative focal lengths, so the power of the lens will also be negative

Note
For a concave lens, the focal length will be negative and in the power formula, the value of the focal length should be only in meters. Before substituting the value in the formula, convert the given focal length from centimeters to meters.