Question

Define power of a lens. What is its unit? One student uses a lens of focal length 50 cm and another of –50 cm. What is the nature of the lens and its power used by each of them?
NCERT Class X
Science - Exemplar Problems
Chapter_Light – Reflection and Refraction

Answer 1

the power of a lens is defined as reciprocal of it's focal length,expressed in meters
p=1/f(in metres)
unit is dioptre(D)
focal length=0.5m so power = 2
as it is +ve so it is real
and focal length=-0.5m so power =-2
indicates virtual image

Answer 2

Power is defined as the "ability of" a lens to "converge or diverge" a beam of light rays. "It is denoted" by P

We know that,

$\mathrm{P}=1 / \mathrm{f}$

The "SI unit of power" of "lens is Dioptre". It is "denoted by" the letter "D".

The SI unit of length is metre(m)

Therefore,

$1 \mathrm{D}=1 / \mathrm{m} \text { or } 1 \mathrm{D}=1 \mathrm{m}^{-1}$

$f_1 = 50cm = 0.5m$

$P_1=1 / f_1$

$P_1=1 / 0.5$

$P_1 = 2D$

Here the power 'P' is positive value. Therefore the lens with focal length 50 cm is convex lens.

$f_2 = -50cm = -0.5m$

$\mathrm{P_2} =1 / \mathrm{f_2}$

$P_2=1/-0.5$

P_2 = -2D

Here the Power is negative value. Therefore the lens with focal length -50 cm is concave lens.

The image which is formed by the concave lens is virtual, erect and diminished irrespective of the "position of the object".