# Power of two lenses

1. Sep 23, 2013

### Aelo

1. The problem statement, all variables and given/known data
Design a thin-lens telephoto lens with a back focal distance of 50 mm and an effective focal length of 200 mm, and a maximum system length (distance between first lens and image) of 100 mm. Find the power of each of the two lenses. (Lenses are in air.)

2. Relevant equations

Power, K = 1/(focal length, f)
Max system length = d + l', where d is the distance between the two lenses and l' is the distance from the second lens to the image. (This is not an equation I "know" - I came up with it myself, so it could be faulty.)

3. The attempt at a solution

I know of only two equations with the effective focal length - one comes from constructing the system vertex matrix (AKA ABCD), and the other comes from doing a paraxial ray tracing (AKA YNU). However, I don't believe I have enough information to use either method, although - making a guess - I would say that I would use the vertex matrix method. There are more equations for that, which I've attached in an image.

Using the given effective focal length and the BFD, I could find the Av element of the matrix. But with both d and l' unknown, I don't know how I could use that to solve for either K.

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