# Calculating EFL of a Three Lens System

1. May 11, 2010

### nek26

If I have three lenses, each one 50 mm in diameter and with focal lengths of 500mm, -125mm and 150 mm, What would be the EFL if I combined them all together (assuming zero distance between them).

I have been looking online for focal lengths of three lens systems but cannot find anything. Would I just use the 1/f = 1/f1 + 1/f2 equation twice and basically turn two of the lenses into one focal length then use that focal length again with the third? Thanks.

2. May 11, 2010

### Bob S

Here is the general matrix solution to a three lens system with arbitrary drifts between the lenses. A drift of length d is represented by a 2 x 2 matrix

1 d
0 1

and a thin lens is represented by

1 0
k 1

where k=-1/f.

I show the matrix equations, and a solution for three 25-cm FL lenses separated by two 2-cm drifts. For your case with no spacing between the lenses, the focus is 150 cm beyond the last lens. If the spacing between the lenses is 1 cm, the focal length is reduced to 96 cm. If the spacing is 0.1 cm, the focal length is 141.5 cm.

Bob S

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Last edited: May 12, 2010