Question

A movie star catches a reporter shooting pictures of
her at home. She claims the reporter was trespassing. To
prove her point, she gives as evidence the film she seized.
Her 1.75 m height is 8.25 mm high on the film, and the focal
length of the camera lens was 220 mm. How far away from
the subject was the reporter standing?

Answer 1

Using lens equation and Magnification

M = Magnification = hi/ho = -v/u

hi = height of image = -8.25 mm = -0.00825 m

ho = height of object = 1.75 m

u = object distance

v = image distance

So,

M = -0.00825/1.75 = -v/u

u = v*(1.75)/0.00825 = 212.12*v

Now given that

f = focal length of lens = 220 mm

So, Using lens equation

1/f = 1/u + 1/v

1/f = 1/v + 1/(212.12*v)

1/f = (1/v)*(213.12/212.12)

v = f*213.12/212.12

Using value of 'f'

v = 220*213.12/212.12 = 221.04 mm

u = 212.12*v = 212.12*221.04

u = -46887 mm

u = -46.887 m = 46.9 m

So the reporter was standing at 46.9 m from the actor.

Please Upvote.