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 in landscape orientation

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?

4.3 metres

My mathematical gut feeling says this is wrong... but it seems about right when I hold the 50mm up to my eye.

70mm lens

theta = 17 degrees

working distance = 180 / tan(17)
                 = 180 / 0.306
                 = 588cm

5.9 metres

135mm lens

theta = 9 degrees

working distance = 180 / tan(9)
                 = 180 / 0.158
                 = 1136cm

11.3 metres

200mm lens

theta = 6 degrees

working distance = 180 / tan(6)
                 = 180 / 0.105
                 = 1712cm

17.1 metres