There are some guidelines for theater & auditorium applications using video & text projections.
The eye can detect 1 minute of arc (1/60 of a degree). For legibility, you need about 10 minutes of arc. The ANSI standard is 16 minutes of arc minimum, and recommends 20-22 minutes. Some of the increase is due to the viewer being off-axis in an audience. It is also for normal 20/20 vision.
The video guidelines are based on image height and the min & max distance to the screen.
All that said, you could use the text guidelines as a bogey if you have nothing else:
At 5 ft: 16 minutes of arc = 0.28 inches, 21 minutes of arc = 0.37 inches
At 10 ft: 16 minutes of arc = 0.56 inches, 21 minutes of arc = 0.73 inches
At 15 ft: 16 minutes of arc = 0.84 inches, 21 minutes of arc = 1.10 inches