Question

Define 1 dioptre power of a lens.

Answer 1

Hint: To get the solution for this question, first understand the definition of power of lens, after the definition is clear it will be easy to understand what dioptre is, as dioptre is the SI unit of power of lens. So, to get the value of 1 dioptre, we need to understand the formula of power of the lens and on what factors it is dependent on, then getting the value for 1 dioptre becomes easy.

Formula used:
$\text{Power, }P\,=\,\dfrac{1}{\text{Focal}\,\text{Length}\,(f)}$

Complete solution:
Power of the lens is the ability of a lens to converge the rays falling on the lens. Power of a lens is defined as the reciprocal of the focal length. Power of lens is measured in Dioptres (D).
The value of 1 dioptre is the power of lens whose focal length is $1\,m$, which means,
$\therefore \text{Power, }P\,=\,\dfrac{1}{f=1}=1=1\,D$

Additional Information:
Optical power (also referred to as dioptric power, refractive power, focusing power, or convergence power) is the degree to which a lens, mirror, or other optical system converges or diverges light. It is equal to the reciprocal of the focal length of the device. High optical power corresponds to short focal length. The SI unit for optical power is the inverse metre, which is commonly called the dioptre.

Note:
The power of the lens is dependent on the value of focal length, which in turn is dependent on the type of lenses that is being used. Converging (convex) lenses have positive focal lengths, so they also have positive power of lens value. Diverging (concave) lenses have negative focal lengths, so they also have negative power values.