Question

From a distance of 72.9m, a photographer uses a telephoto lens (f = 300mm) to take a picture of a charging rhinoceros. How far from the rhinoceros would the photographer have to be to record an image of the same size using a lens whose focal length is 53.0mm?

Answer 1

image distance for a telephoto lens is

1/di + 1/do = 1/f

1/di = 1/f - 1/do

1/di = 1/0.3 - 1/72.9

di = 0.3 m

then image size is di/do = 0.30 / 72.9

Again the image distance for the lens of focal length 53 mm

1/di = 1/0.053 - 1/do ............(1)

in this case image size must be di/do = 0.30 / 72.9

di = (0.30 / 72.9)do

Now (1) becomes

(72.9 / 0.30*do) = 1 / 0.053 - 1/do

[(72.9 / 0.30) + 1] x 1/do = 1/0.053

244 x 1/do = 18.87

do = 12.932 m is the required distance..