There are at least two ways to do this. Here is the simpler, more intuitive approach.If you take a picture of the same scene, one with a 35mm lens, and the other with an 85mm lens, how exactly would you position the prints so that the perspective would be the same, with relation to the viewer?
The original scene perspective is preserved if we view a print the size of the negative at the same distance as the focal length of the lens used to photograph the scene for infinity focus.
Using the focal length of the lens is good enough for most approximations at mid-distance to infinity-focus shots. If you require greater accuracy you can use the focus distance and the focal length to calculate the lens-to-negative distance. This is the actual viewing distance for correct perspective. Here’s a 35mm format example.
Most of us don’t want to view a 24mm x 36mm print from 50mm or whatever the focal length used. But we can magnify the print size and viewing distance until we get something practical.
Use the focal length f and let
v = viewing distance
w = width of the projection of the 24mm negative dimension in enlargement
For the 35mm lens on the 35mm format we have
v/w = 35/24, so
v = (35/24)*w
If we choose a projection width of 16.5” to make a 16” x 20” print
v = (35/24)*16.5” = 24” viewing distance.
For the 85mm lens on the 35mm format with 16.5” wide projection of the 24mm width of the negative
v = (85/24)*16.5” = 58.4” viewing distance.
Viewing the print at the correct-perspective viewing distance preserves the angular relationships that existed at the camera’s lens position. For example, the on-print images of two objects that were 10° apart in the scene at the camera position will subtend 10° at the viewing distance v.
Of course this can be done for any format. Alternatively, you could fix the viewing distance and size the projection to suit as
w = (24/35)v