A few weeks ago, armed with a pair of 200mm Achromat lens elements, I started work on a second Dollar Bill Lens. I wanted to see if 2 elements, with an aperture placed between them, would give me better images than the single lens element $1 Dollar Bill Lens. Now, I know that these are already solved riddles. All I have to do is ask someone who knows.
But...what's the fun in that? It's just so much more enjoyable experimenting, seeing what happens, than looking it up. Plus one of the things I like the most past the toying around is the unexpected. It's within the unexpected that I personally think the best images come from. The combination of methodical control and unexpected chaos is addicting. That's how I shoot 4x5. It isn't what Ansel Adams would have done, by a long shot but...I'm not him, so there you have it.
So I placed the two elements together within four $1 bills in order to start mocking up the construction. Math wise, everything worked out to a 104mm lens with a 95mm BFL.
Achromat lens elements in question: http://www.surplusshed.com/pages/item/b1108.html
The math, in case you're interested:
Focal Length (f1 = front lens, f2 = back lens, d = distance between them)
F = (f1 x f2) / (f1 + f2 - d)
F = (200x200) / (200+200-19)
F = 40000 / 381
F = 104mm
Back Focal Length (f1 = back lens, f2 = front lens, d = distance between them)
BFL = (f2 x (d - f1)) / (d - (f1 + f2))
BFL = (200 x (19 - 200)) / (19 - (200 + 200))
BFL = -36200 / -381
BFL = 95mm
Yet, when I put them together and mount the resulting lens on my 4x5, the BFL was way, way off. As in it didn't show a sharp image on the ground glass until it was brought almost all the way within an inch of the ground glass. So out of curiosity I took one out and left the other one in. With a single lens, the BFL should match the FL. In that scenario the FL was acting more like a 40mm or 45mm lens. I've did this with and without the flint piece, and also with the flint on both sides of the lens just to be sure I wasn't missing something really basic. The result was the same.
Puzzled, I emailed all of my math and findings to a Professor of mine from the Rochester Institute of Technology (RIT), Andrew Davidhazy. Prof. Davidhazy taught very, very, VERY technically oriented photography subjects and is renowned for his high speed stop motion image captures. He was kind enough to take a look, ask for a clarification or two, and then conclude: "I'd say that you did not get 200 mm lenses..."
And this is where awesome customer service comes in. I emailed the whole shebang to Surplus Shed. One of their team replied on his day off, told me he'd check the lenses the next day. After doing so, and after finding that the lenses had come from a mislabelled military surplus lot, immediately found the closest lenses they had in stock to what I wanted and shipped them my way for free. I could keep the originals, no worries, no issues.
The 195mm lenses will arrive today. I can't wait to take another crack at the $4 Dollar Bill Lens, just in time for the weekend!