# Optics and lens

hey, i tried the following problem and i think i got it wrong well. here is the problem and what i did.

problem
A photograph of a zebra is taken from a distance of 100m with a 50mm lens. A second picture is taken from a distance of 50m with the same lens. What is the ratio of the height of the image in the second picture to the height in the first picture?

What i did
well. its obvious that the ratio is 2:1 because the distance of image int eh 100m to the distance of the 50m picture is 2:1 and the fact that it uses the same lens proves it. but my main issue with the problem is that i cant understand weather the 50mm lens can be used as the focal length of the problem. well I used it and here is what i got:

for the 100m:
1/f = 1/do + 1/di

so: 1/0.050 = 1/100 + 1/di

5di/0.050 = 5di/100 + 5di/di

100di = 0.05di + 5

100di - 0.05di = 5

99.95di = 5

99.95di/99.95 = 5/99.95

Therefore: di = 0.050025012

Note: to get the height of the image or object the equation is:

M = hi/ho = -di/do

I have the di and do but I don’t understand how I get hi or ho
M is the magnification

For the 50m:

1/f = 1/do + 1/di

So: 1/0.050 = 1/50 + 1/di

2.5di/0.050 = 2.5di/50 + 2.5di/di
50di = 0.050di + 2.5

50di – 0.050di = 2.5

49.95di = 2.5

49.95di/49.95 = 2.5/49.95

Therefore: di = 0.05005005

..here is the confusing part: the di of the 100 its half of the di or the 50 which I think it should be, and I don’t see how I can get the highet of the image.?

Diane_
Homework Helper
Would it help to point out that the height of the object remains the same in both cases?

ok

i know that the ho reamains the same but i dont know how i can show the relation between both cases? i dont understand how to get the ratio.

edit: here is what i did..tell me if it is right

case1
hi/ho = 0.050025012/100

hi/ho = 0.0005052012

case2
hi/ho = 0.05005005/50

hi/ho = 0.001001001

0.001001001/0.0005052012