Question

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

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:

The ratio of focal length of two convex lenses is 1 : 5.

To find:

Ratio of power ?

Calculation:

• Power of lens is defined as the converging or diverging power of any lens.

• Let the focal lengths be x and 5x.

So, ratio of power will be :

$\dfrac{P_{1}}{P_{2}} = \dfrac{ (\dfrac{1}{ f_{1} } )}{ (\dfrac{1}{ f_{2} }) }$

$\implies \dfrac{P_{1}}{P_{2}} = \dfrac{ f_{2}}{ f_{1} }$

$\implies \dfrac{P_{1}}{P_{2}} = \dfrac{ 5x}{ x }$

$\implies \dfrac{P_{1}}{P_{2}} = \dfrac{ 5}{ 1}$

So, required ratio is P1 : P2 = 5 : 1.