Question

If the ratio of focal length of two convex lenses is 1: 5 then what is the ratio of their power?​

Answer 1

Question-

If the ratio of the focal length of two convex lenses is 1 : 5 then what is the ratio of their power?​

Answer-

The power of a lens is defined as the reciprocal of its focal length in meters, or D = 1/f, where D is the power in diopters and f is the focal length in meters.

Let the focal length of two convex lenses be 1x and 5x respectively.

Then,

The power of first convex lens = 1/1x = 1x

The power of second convex lens = 1/5x = 0.2x

The ratio so formed is-

1x : 0.2x

⇒ 5 : 1

The ratio of the power is 5 : 1

Answer 2

Given:

Ratio of focal length of lens is 1 : 5.

To find:

Ratio of their power ?

Calculation:

• Power refers to the converging or diverging capability of any lens. In other words, it is the reciprocal of focal (in metres).

• Let focal lengths be x and 5x

So, ratio of power will be :

$\dfrac{P1}{P2} = \dfrac{ \dfrac{1}{x} }{ \dfrac{1}{5x} }$

$\implies \dfrac{P1}{P2} = \dfrac{ 5x }{ x }$

$\implies \dfrac{P1}{P2} = 5$

$\implies P1 : P2= 5 : 1$

So, ratio of powers is 5 : 1.