Again, my math may be suspect, but for my iPhone 5 where the vertical field of view is ~58.5°, the horizontal field of view should be ~45.56°. Keep in mind that the horizontal and vertical dimensions are the opposite of film. So the vertical dimension is the long one and the horizontal is the short one.
2*tan(22.78°)*d, where d equals the distance from the edge of my desk to my laptop screen as measured by a legal pad is 11 inches. The formula gives me a 9.25" distance required between the two shots. The distance actually required appears to be about 8.5"
This doesn't help much because there are no official numbers published on the iPhone 5's back camera field of view and I have seen varying numbers posted on the internet. Also, I am not measuring with any precision or guarantee that the angle of the phone is not changing slightly between shots. Anyway, it seems reasonably close to me, but I will check with my actual camera when I get home.
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