Here’s the more accurate answer
First part of problem. The f/# defines the cone angle in the image space. You can back out the answer that the marginal ray height at the 150mm f/22 lens is 3.41mm (paraxial approximation fine for this f/#).
See first pic showing calculation
From there the marginal ray travels to the corner of the film, 3.05” or 77.47mm off-axis for 4x5.
Similar triangles means the distance from stop to the end of the 80mm diameter cylinder closest to the film plane is readily calculated. See second pic. You should measure from the film plane since you don’t know the actual stop position relative to the lens mount.
That distance is 75.89mm from film to the back of the tube. See second pic. Pere’s calculation is close, but small errors can be critical when designing system baffling to control stray light (one of the few optical design lessons I’ve learned the easy way), so it’s worth being accurate.
The calculations don’t account for shifts nor for closer focus than infinity ... that can be accommodated by incorporating magnification factor to determine marginal ray height and back focal distance.
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