Let's Plug In Some Numbers

Let's look at the resulting F and BFL values for some combinations of two lenses.

Keep the formulas in mind:
      F = (f1 x f2) / (f1 + f2 - d)
      BFL = (f2 x (d - f1)) / (d - (f1 + f2))

#   LENS #1 LENS #2 DIST     F       BFL    
1 100 100 0 50 50  
2 100 100 50 67 33  
 
3 100 200 50 80 40  
4 200 100 50 80 60  
 
5 -200 100 50 133 167 Retrofocus
6 100 -200 50 133 67 Telephoto

Lines 1 and 2 show the affect of the distance between the element when using two positive lenses.

Lines 3 and 4 show how the focal lengths affect the results when using two positive lenses.

Things get much more interesting when one of the lenses has a negative focal length.

If the light passes through the negative lens first, we get a combination in which the focal length is less than the BFL (Line 5). This retrofocus comfiguration is useful for making wide angle lenses.

If the light passes through the positive lens first, we get a combination in which the focal lemgth is longer than the BFL (Line 6). This telephoto comfiguration is useful for making long focal length lenses.

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