The magnification of a lens with focal length 55 mm at a distance of 100 m is m = 0.0005506. To calculate it, follow the steps:
Calculate r = sqrt(d²/4 - f × d) = 49.945.
Calculate:
The distance between the object and lens: g = d/2 + r = 99.945; and
The distance between the lens and sensor: h = d/2 - r = 0.05503.
Compute the magnification with the ratio m = h/g = 0.0005506.
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