Question

From a distance of 70.0m, a photographer uses a telephoto lens (f = 250mm) 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 52.0mm?

Answer 1

Solution :-

Given f = 250mm

         d_o = 70 m

We know the formula is ( 1 / f ) = ( 1 / d_o ) + ( 1/ d_i )

And the formula for the magnification is

                     m = - d_i / d_o   

                      d_i = - md_o    

Now ( 1 / f ) = ( 1 / d_o ) + ( 1 / d_i)

          ( 1 / f) = ( 1 / d_o ) + ( 1 / -md_o)   

                   = ( 1 / d_o )[ 1- (1/m)].............................(1)

In the second situation f' = 52.0mm

                                     d'_o = ?     

Now   ( 1 / f' ) = ( 1 / d'_o )[1- (1/m)].............................(2)     

Now dividing the eq(1) and (2) we get

                f' / f = d'_o /d_o ........................(3)

Now substitute the values of f' f' and d_o in theeq(3) we get the value ofd'_o