From a distance of 90 m a photographer uses a telephoto lens

From a distance of 90 m, a photographer uses a telephoto lens (f = 495 mm) to take a picture of a charging rhinoceros. How far from the beast would the photographer have to be to record an image of the same size using a lens whose focal length is only 85 mm?

Solution

Ans: 14.689 m

Explanation : Since the telephoto lense arrangement can be simplified by considering an equivalent convex lense, thin lense assumption will be valid, hence thin lense formula can be applied

formula is 1/v - 1/u =1/f eq1

and magnification=-v/u eq2

for same size of image, magnification needs to be kept same, i.e the ratio of image and object distance has to be kept same.

Now, for the telephoto lense v and f are known. So using eq1 &2 one can find u and hence magnification m.

For the the second lense m is known=> value of v can be calculated using eq1 which will be the answer.