Following up on our tale of shooting an iris through a pinhole, we wanted to ask a question: How much smaller?
As we mentioned, we used an aperture ("aperture" is a pretentious word for "hole") that was small - a little less than one square millimeter. But, as Dad would say, "Compared to what?" How much smaller was that "pinhole" than the usual photographer's hole, or the biggest possible photographer's hole?
The formula for hole size is area = π (f/2N)2 (where f is the focal length, and N is the f-number). So, using a 60 mm lens at f/57, the hole was 0.87 mm2; but with that lens fully open at f/2.8, the hole would be 361 mm2 (a bit more than half a square inch), which is about 414 times bigger.
So, you could say, that to get that shot, we shrunk the hole by about a factor of 414.
Comment: (57/2.8)2 = 414.413...