Question

If the power of of the lenses L1 and L2 are in the ratio of 4:1 , what would be the ratio of the focal length of L1 and L2?​

Answer 1

Answer:

1:4 P1:P2=4:1 P1=1/F1 = 0.25 and P2=1/F2 = 1 0.25 Or 25/100= 1:4

Answer 2

Given,

Ratio of power of the lenses L1 and L2 is 4:1

To find,

Ratio of focal lengths of L1 and L2.

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

Here, we need the following mathematical relationship between the power and focal length of a lens.

Power of a lens = 1/focal length

or, focal length = 1/Power of a lens

Now, from the given ratio of powers of the lenses, let the power of,

L1 = 4x dioptre

L2 = x dioptre

According to the previously mentioned, mathematical relationship between power and focal length.

Focal length of L1 = 1/4x metre

Focal length of L2 = 1/x metre

Their ratio = 1/4x : 1/x = 1/4x × x/1 = 1/4 = 1:4

Hence, the ratio of their focal lengths will be 1:4