Question

For two concave lenses A and B of focal lengths 12 cm and 18 cm, the ratio of the powers (A to B ) is

Answer 1

Answer:

The correct ratio is 3:2

Explanation:

As per the formula,

The power of a lens is the reciprocal value of its focal length and is measured in Diopters.

So the lens having 12cm focal length has power = -1/12D ( As focal lengths of concave lenses have negative value in air)

and that of lens having 18cm focal length is = -1/18D

So the ratio will be -1/12

-1/18

= 18/12 = 3/2 = 3:2

Answer 2

To find the ratio of power of concave lenses follow the steps as shown:

Given:

focal length of concave lens A = 12 cm = 0.12 m

focal length of concave lens B = 18 cm = 0.18 m                                                  (∵ focal length should be in metres to calculate power in dioptre)

To Find:

Ratio of Power of lens (A : B) = ?

Step wise solution:

The power of lens is the reciprocal of its focal length. It is denoted as 'D' and expressed in Dioptre.

To calculate the power of lens apply following formula:

Power (D) = 1 ÷ f (in metres)

Power of lens A = -(1 ÷ 0.12 m)

Power of lens B = - (1 ÷ 0.18 m)

(∵ The power of concave lens is negative as the image is formed behind the mirror)

Ratio of power of the lens (A : B) = -(1 ÷ 0.12 m) ÷( - (1 ÷ 0.18 m))

                                           (A : B) = 0.18 ÷ 0.12

                                          (A : B) = 3 : 2

Hence, the ratio of power of lens A : B is 3 : 2.