# ^Combination of lenses

^**Combination of lenses**

Two or more lenses are combined to

- Increase magnification.
- Make final image erect.
- Reduce certain aberrations.

#### If two thin lenses of focal lengths f_{1} and f_{2} are separated by a distance d then the effective focal length and power of the combination is given by:

1.

2. P = P_{1} + P_{2 }– d P_{1} P_{2 }

3. m = m_{1 }x m_{2 }x m_{3 }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.