^Combination of lenses

Two or more lenses are combined to

1. Increase magnification.
2. Make final image erect.
3. Reduce certain aberrations.

If two thin lenses of focal lengths f₁ and f₂ are separated by a distance d then the effective focal length and power of the combination is given by:

1.

2. P = P₁ + P₂ – d P₁ P₂

3. m = m₁ x  m₂  x  m₃  x – – – – – – – – –

Let us prove the above relations.

* A Zoom lens is based on this result such that f can be varied 0 to ∞ by changing d.