# Optics - distance between object and image

Smile101
hello,

## Homework Statement

A lens has a focal length of 20 cm and a magnification of 4. How far apart are the object and the image?

## Homework Equations

m=di(image)/do(object)
1/di + 1/do = 1/f

## The Attempt at a Solution

Well, I don't really know what to do, I feel like I don't have enough information. Your help will be very appreciated!

Staff Emeritus
Homework Helper

Since you have 2 equations in 2 unknowns ... solve 1 equation for 1 of the unknowns, then substitute that into the 2nd equation.

Smile101

Since you have 2 equations in 2 unknowns ... solve 1 equation for 1 of the unknowns, then substitute that into the 2nd equation.

Yes, I was thinking about that but how do I do it? Seeing as if i did m=di/do 4=di/do --but it leads me to a dead end

or if i used 1/di+1/do=1/f i can only go as far as 1/di+1/do=1/20 then once again i get to a dead end!

Staff Emeritus
Homework Helper

4=di/do

Okay, so far so good. Now solve that equation for di:

di = _____ ?​

Smile101

Okay, so far so good. Now solve that equation for di:

di = _____ ?​

umm.. di=4(do) but since we don't have do we can't solve for di

Staff Emeritus
Homework Helper

umm.. di=4(do) but since we don't have do we can't solve for di

You can now substitute 4do for di in the other equation ... that eliminates di, leaving do as the only unknown.

Smile101

You can now substitute 4do for di in the other equation ... that eliminates di, leaving do as the only unknown.

so the equation is : 1/di +1/do =1/f

1/4do + 1/do = 1/20

Now I'm guessing we want to make do single... but i have to get rid of the 4 so since I'm dividing...

1/do^2 = 1/20 - 1/4

Homework Helper

so the equation is : 1/di +1/do =1/f

1/4do + 1/do = 1/20
Multiply do to both sides and solve for do.

Staff Emeritus
Homework Helper

Multiply do to both sides and solve for do.

Yes, exactly. It's just algebra at this point.

Smile101

sorry for the late reply but, thanks a lot for your help, I really appreciated it! :)