Question

The focal length of a convex lens is $25\;{\text{cm}}$. Find its power with a sign.
A) $ + 4\;{\text{D}}$
B) $ - 4\;{\text{D}}$
C) $ + 2.5\;{\text{D}}$
D) $ - 2.5\;{\text{D}}$

Answer 1

Hint:In this question, use the concept of the convex lens that is the sign convention for the focal length of the convex lens. First, we discuss the power of lenses. Then provide the sign convention used for convex lens and concave lens. Convert the focal length in the proper unit and calculate the power of the lens.

Complete step by step solution:
We define the power of a lens as the reciprocal of the focal length of the lens. So, the power of lens is expressed as $P = \dfrac{1}{f}$
Where, $f$ is the focal length and it is expressed in meters.
So, the unit of power of the lens is expressed in ${{\text{m}}^{ - 1}}$. This is also expressed as diopter.
As we know that the focal length of a convex lens is taken as in positive sign and focal length of a concave lens is taken negative. So, the power of a convex lens is positive, and the power of a concave lens is negative.
In this question it is given that the lens is convex, and its focal length is $25$ cm. First we will convert the focal length in meters.
$ \Rightarrow 25\,{\text{cm}} = 0.25\,\,{\text{m}}$
Now, substituting the value of focal length in the formula of power of lens we get
$P = \dfrac{1}{{0.25}}\,{{\text{m}}^{ - 1}}$
$ \Rightarrow P = 4\,{{\text{m}}^{{\text{ - 1}}}}$
${{\text{m}}^{ - {\text{1}}}}$ is also expressed as diopters or $D$
As it is a convex lens so its power is positive.
Thus, the power of the lens is $+ 4D$.

Hence, the correct option is A.

Note: As the power of lens is reciprocal to its focal length. So a lens with less focal length is said to have more power. The power of various lenses in contact is equal to the algebraic sum of powers of those individual lenses.