Question

$ 1{\text{ D}} $ is equal to:
(A) $ 1m $
(B) $ 1cm $
(C) $ 1{m^{ - 1}} $
(D) $ 1c{m^{ - 1}} $

Answer 1

Hint : To solve this question we need to identify the quantity whose unit is one dioptre. Then we have to use its basic formula to find out its unit in the form of the options which are given to us.

Formula used: The formula which is used to solve this question is given by
 $ P = \dfrac{1}{f} $ , here $ P $ is the optical power of a mirror or a lens whose focal length is $ f $ .

Complete step by step answer
 $ {\text{D}} $ in $ {\text{1 D}} $ stands for the unit ‘Dioptre’. One dioptre is the SI unit for the measurement power of a curved mirror or a lens. We know that the power of a mirror or a lens is defined as its ability to bend the light ray which is incident on its surface. It is equal to the inverse of the focal length of the mirror or the lens. So it is given by the formula
 $ P = \dfrac{1}{f} $ .......................(1)
Now, we know that $ f $ is the focal length. So, its SI unit should be meter. Therefore, from (1) the SI unit of the power is given as $ \dfrac{1}{m} $ or $ {m^{ - 1}} $ . Since the SI unit of power is taken as one dioptre, so $ 1{\text{ D}} $ is given by
 $ 1{\text{ D}} = {m^{ - 1}} $
Or
 $ 1{\text{ D}} = 1{m^{ - 1}} $
Thus, $ 1{\text{ D}} $ is equal to $ 1{m^{ - 1}} $ .
Hence, the correct answer is option C.

Note
The unit Dioptre of the power is used in the prescription of the corrective eye lenses by the eye care professionals for the correction to the eye sight. Also, the dioptre is used in the measurement of curvature of a curve, which is equal to the inverse of the radius. The unit of curvature is taken to be dioptre.