Find the object focal point for a combination of two thin le

Find the object focal point for a combination of two thin lenses whose individual object focal points coincide.

Solution

We have two lens kept togther such that the focal points of each of the lens coincide.

Now, for any far away object, the image formed by the first lens would be at its focal length.

That is for the first lens we can write:

1 / d_o + 1/d_i = 1/f₁

Now, d_o = , so we get:

1 / d_i = 1/f₁

now, the image distance in this case would be same as the focal length, however, it would also be the the focal point for the second lens, we can write for the second lens:

1/d_o + 1/d_i = 1/f₂

However, the do in this case would be negative as it would be virtual object, hence giving us:

1/ d_i = 1/f₁ + 1/f₂ [Since do in this case would be f1]

Now, we can say that for any far object, the image is formed at the distance given as: 1/ f₁ + 1/f₂

Therefore the combined focal length of the combination would be given as:

1/f = 1/ f₁ + 1/f₂