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

{{attachment:50mm_triangle.png}}

{{{
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'''