Hyperfocal distance with cropped image cheatsheet

TLDR: Hyperfocal distance is proportional to enlargement.

What happens to the hyperfocal distance if you intend to print a crop at the same size for the same viewing distance?

Back to basic assumptions:

• Visual acuity of 5lp/mm at 25cm viewing distance. This is equivalent to a final print circle of confusion of 0.2mm.
• Print size is 8x12. Enlargement = 12"/36mm = 8.47. Circle of confusion = 0.2mm/8.47 = 0.0236mm.
• If you crop and print at the same size, you increase enlargement and decrease the circle of confusion.

Hyperfocal distance is inversely proportional to circle of confusion and is proportional to enlargement.

Example:

35mm full frame fixed focal length camera

f8.0 aperture

8x12 print size

Hyperfocal distance = 35 * 35 / 8 / 0.0236 = 6.5m.

With 1.5x crop (simulated 52mm), hyperfocal distance = 9.7m.

With 2x crop (simulated 70mm), hyperfocal distance = 13m.

Caveat:

Viewing distance is traditionally supposed to depend on the focal length (to get the same perspective), but these days, everything is viewed at phone distance :)