Question

What is meant by the power of a lens? State its SI unit. What do their positive and negative signs indicate?

Answer 1

The power of a lens is one of its most important parameters that is in fact used as the parameter for prescribing all corrective lenses. The power of a lens is inversely related to its focal length and can be written mathematically in terms of it.

Formula used:
$P=\dfrac{1}{f}$

Complete step-by-step answer:
The power of a lens is an important parameter of it that determines the ability of a lens to converge (for convex lens) or diverge (for concave lens) light rays that pass through the lens.
The greater the ability of the lens to diverge (for concave lens) or converge (for convex lens) light rays passing through it, greater will be the power of the lens.
The power $P$ of a lens can be written mathematically as the inverse of its focal length $f$.
$P=\dfrac{1}{f}$ --(1)
The SI unit of power is dioptre $\left( D \right)$ which is the inverse of the focal length written in metre $\left( m \right)$.
$1D=\dfrac{1}{1m}=1{{m}^{-1}}$
If the power of a lens is positive, from formula (1), it inherently means that the focal length of the lens is positive. This means that the lens is a convex lens since a convex lens has a positive focal length.
If the power of a lens is negative, from formula (1), it inherently means that the focal length of the lens is negative. This means that the lens is a concave lens since a concave lens has a negative focal length.

Note: Students should keep in mind that while writing the power in dioptres, they should write the focal length in meters. Usually, in optics the focal lengths of lenses are expressed in centimeters $\left( cm \right)$, since the unit is more convenient for this purpose and the meter can be an inconveniently large unit to handle. However, when writing the power in dioptres, students must convert the focal lengths from centimeters to meters.