Pfeiffer Duckett

13-Feb-2008, 01:00

I have a mathematical problem that I am having trouble with. It isn't very hard, I've just forgotten my schooling.

Here it goes: Lets say a lens only has coverage for 2x3 inch film when focused at infinity. Using the pythagorean theorem you can get a reasonable idea of what the diameter of the image circle would be: (the square root of two squared plus 3 squared so 3.6056). Divide that if half to get the radius, and using trigonometry and the theoretical length of the lens combined with the radius of the image circle, you should be able to find the angle of view.

Let us then say that you want the lens to cover 4x5. Using the pythagorean theorem again, you find that the image circle needs to be 6.4031 inches in diameter or, alternatively, have a 3.2016 inch radius. Using the angle of view that was found in the last problem and the radius, you should be able to find out how far away the lens needs to be from the plane of focus to cover the larger film format, and thereby find out how close the subject would have to be for the image to be both in focus and cover the film.

I want to see how far away from the film a lens with a focal length of 100mm which covers 6x9 cm would have to be to cover the 4x5 inch format- with bonus points for a theoretical distance of how close the subject would have to be.

My problem is that I have forgotten most of my trigonometry in leu of photo theory, and I sold my TI-83 for film long ago. If somebody who retained this information could help me out on this I would be very grateful.

~Pfeiffer

Here it goes: Lets say a lens only has coverage for 2x3 inch film when focused at infinity. Using the pythagorean theorem you can get a reasonable idea of what the diameter of the image circle would be: (the square root of two squared plus 3 squared so 3.6056). Divide that if half to get the radius, and using trigonometry and the theoretical length of the lens combined with the radius of the image circle, you should be able to find the angle of view.

Let us then say that you want the lens to cover 4x5. Using the pythagorean theorem again, you find that the image circle needs to be 6.4031 inches in diameter or, alternatively, have a 3.2016 inch radius. Using the angle of view that was found in the last problem and the radius, you should be able to find out how far away the lens needs to be from the plane of focus to cover the larger film format, and thereby find out how close the subject would have to be for the image to be both in focus and cover the film.

I want to see how far away from the film a lens with a focal length of 100mm which covers 6x9 cm would have to be to cover the 4x5 inch format- with bonus points for a theoretical distance of how close the subject would have to be.

My problem is that I have forgotten most of my trigonometry in leu of photo theory, and I sold my TI-83 for film long ago. If somebody who retained this information could help me out on this I would be very grateful.

~Pfeiffer