Stats for a full-frame 35mm camera, taken from lens manufacturers' spec sheets.
- 50mm = 46 degrees
- 70mm = 34 degrees
- 135mm = 18 degrees
- 200mm = 12 degrees
Now, those are presumably across a circular diameter (ie. the diagonal of a frame).
For a 3m wide backdrop, your hypotenuse in 3:2 aspect ratio is sqrt(13), or 3.6m.
Now use some trig to convert those angles into 3.6m.
Working
For a 50mm lens:
- theta = 23 degrees
- Opposite = 180cm
tan(23 degrees) = 180 / working distance 0.42 = 180 / working distance 1/0.42 = working distance / 180 180/0.42 = working distance working distance = 428cm?
I don't think this is correct...