When is the focal length same as the distance to the image? Need to prove mathmatically?

Question

I need this question to be proven mathematically.
Thanx~!!

Answer 1

When the image is infinitely far away, 1/s+1/o=1/f. If o=infinity 1/s=1/f or s=f, image distance = focal length.

Answer 2

Definition of focal length: Focal length is the distance between a lens and the image it creates of a far-away object.

So your answer is, image distance = image distance when the object is far away.

If you want an equation:

1/o + 1/i = 1/f

so 1/i = 1/f iff 1/o = 0, so o = infinity.

Answer 3

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