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.