Why is the image distance (3/2)f when object distance is 3f?

[libra10489]

Homework Statement

An object is 3 times further from a a lens than its focal length. Let f rep focal length. How man times the focal length of the lens is the image from the lense? The answer is (3/2)f but I don't understand why. Could someone please explain it to me?

 

[tiny-tim]

welcome to pf!

hi libra10489! welcome to pf!

what equations do you know relating the object distance the image distance and the focal length?

 

[libra10489]

The only one I know is (1/object distance) + (1/image distance) = (1/focal length).

 

[tiny-tim]

that's the one!

ok, now put the numbers in …

what do you get? ​

 

[libra10489]

Um...there are no numbers...if there were numbers I'd be able to plug and chug. I guess the confusing part is "An object is 3 times further from a lens than its focal length."

 

[tiny-tim]

use algebra …

call the focal length "f" …

then the object distance is 3f, so the image distance is … ?

 

[libra10489]

Oh..., now I feel stupid... OK I got it. Thanks.