Question

How are power and focal length of a lens related? You are provided with two lenses of focal lengths of 20 cm and 40 cm respectively. Which lens will you use to obtain more convergent light?

Answer 1

Step1: Focus and Focal length of a lens:

1. Focus is the point at which rays falling perpendicular to the lens converge to a point if the lens is convex and seems to diverge from a point if the lens is concave.
2. The focal length of a lens is defined as the distance from the focus to the optical center.
3. The below figure depicts the above definition.

Step2: Diagram

Step3: Power of a lens:

1. Power of a lens is defined as the reciprocal of the focal length, i.e, $Power\left(D\right)=\frac{1}{focallength\left(f\right)}$
2. Power is measured in dioptres ($D$).

Step4: Explanation:

We know that $Power\left(D\right)=\frac{1}{focallength\left(f\right)}$

Power of the first lens $D_1=\frac{1}{20}D$

Power of the second lens $D_2=\frac{1}{40}D$

Therefore $D_1>D_2$.

1. So the lens having a focal length of 20 cm will converge light more as compared to the length with a focal length of 40 cm.
2. The lens with a focal length of 20 cm will have more power than the lens having a focal length of 40 cm.

Hence the lens with more power will converge light more.