Building a Telephoto Lens
Let's take an example. A while back, I had made a single element 400 mm lens with a long sliding-tube focuser. Now I want to make a lens with an even longer focal length using the same sliding tubes. I'm limited by the lenses I have on hand. I happen to have a positive lens with a focal length of 191 mm and a negative lens with a focal length of -167. That should work.
To find the right distance between the lenses, I could plug these values into the BFL formula, along with a desired BFL of about 400 mm, and solve for d. But today I feel more like "doing" than "thinking", so with a little trial and error, I came up with a distance that allows me to attain focus on distant objects. I measured the distance at 75 mm. According to the formulas this should give me a 625 mm lens with a 380 mm back focal length.
Here's a photo of the lens, complete with a Nikon mount, sliding-tube focuser and an old iris diaphragm. The front element is a +191 mm lens. The rear element is a -167 mm lens. And there is 75 mm separating them.