Question

A thin lens has a focal length of $- 50cm$. What is the power of the lens and its nature?

Answer 1

Hint
In the question, we are given the focal length of a thin lens. The power of a lens can be written as the reciprocal of the focal length expressed in meters. The type of lens can be understood from the sign of the focal length.
Formula used
$P = \dfrac{1}{f}$
Where $P$ stands for the power of the lens and $f$ stands for the focal length of the lens.
Step by step solution:
We know that the focal length of the lens as given in the question is
$f = - 50cm$
Converting into meters,
$f = - 0.5m$
The power of the lens is,
$P = \dfrac{1}{f} = \dfrac{1}{{ - 0.5}} = - 2D$
Since the power is obtained as negative, the lens will be concave.

Additional information
The power of a lens is measured in the units of a dioptre. The power of a lens with a focal length of $1m$ will be $1$ dioptre. In devices like cameras, microscopes, telescopes, and many other optical instruments combination of concave and convex lenses is used. The lenses are also used for correcting various defects of the human eye. Nearsightedness is corrected using a concave lens Another defect of the human eye is called astigmatism. It is corrected by using cylindrical lenses of the desired radius of curvature.

Note
The type of lens can be determined from the sign of the focal length. The distance between the principal focus and the optic centre is called the focal length of the lens. If the power is given as positive then the lens is a convex lens or a converging lens. If the power is negative, then the lens is a concave lens or a diverging lens.