Question

Two lenses, one converging of power 8D, and the other diverging of power 4D, are combined together. Calculate the focal length and power of the combination.

Answer 1

Given

P1=8D

P2=4D

We know that

Power of a combination of lens(P)= p1+p2

=8+4

=12D

Now

F=1/p

F=1/12

Hope it helps u ✌✌✌✌

Answer 2

Given,

Power of a converging lens = 8D

Power of a diverging lens = 4D

To find,

The focal length and power of the combination of both lenses.

Solution,

We can simply solve this numerical problem by using the following process:

Let us assume that the focal length of the converging lens is F1, the focal length of the diverging lens is F2, and the focal length of their combination is F.

Mathematically,

Power of a lens

= 1/(focal length of the lens)

And, if a set of lenses with individual focal lengths as F1, F2, etc, the focal length of the combination (F) is:

1/F = 1/F1 + 1/F2 +...

{equation-1}

Now, according to the question;

Power of the converging lens = +8D

=> 1/F1 = +8D

=> F1 = 1/8 m^-1

And, the power of the diverging lens = -4D

(Since a diverging lens always has a negative focal length, and hence a negative power)

=> 1/F2 = -4D

=> F2 = -1/4 m^-1

Now, according to the equation-1;

1/F = 1/F1 + 1/F2

=> 1/F = 1/F1 + 1/F2 = +8D - 4D = +4D

=> power of the combination of the lens = +4D

=> F = 1/4 m = +25 cm

Hence, the power of the combination of the lens is equal to +4D and its focal length is equal to +25 cm.