# Thin Lens - Object Distance

1. Apr 18, 2014

### ghostops

1. The problem statement, all variables and given/known data
Now consider a diverging lens with focal length f=−15cm, producing an upright image that is 5/9 as tall as the object.
What is the object distance? You will need to use the magnification equation to find a relationship between s and s′s′. Then substitute into the thin lens equation to solve for s.

2. Relevant equations

1) M = -s'/s

2) 1/s+1/s'=1/f

3. The attempt at a solution

using equation 2 I solved for s' then subsituted that into equation 1 and solved for s and from that put it back into equation s and solved for s and ended up with the answer of -65/3.

However this was the wrong answer and do not know what I did wrong.

2. Apr 18, 2014

### Staff: Mentor

And what did you get? Show exactly what you substituted into the equation.

Ditto.

Double ditto. (Well, you've told us the answer you got, but we still need to see exactly how you got it.)

It's hard for us to tell you what you did wrong, if you don't tell us exactly what you did. If you show us all the steps explicitly, we can tell you which step went wrong.

3. Apr 18, 2014

### ghostops

step 1: s = (1/f-1/s')^-1

step 2: m=-s'/((1/f-1/s)^-1)
m=-s'(1/f-1/s)
m=-(s'/f-1)
(f/s')m=1
f/s'=1/m
f=s'/m
s' = f(m)

step 3: 1/s+1/fm=1/f
1/s=1/f-1/fm
s=(f-fm)^-1

4. Apr 18, 2014

### dauto

Double check your algebra. There is at least one fairly serious mistakes there. In step 2, how did you get from the third line to the fourth line?

Last edited: Apr 18, 2014
5. Apr 18, 2014

### Staff: Mentor

Check this step carefully. I added an intermediate step in red to (hopefully) make the error more obvious.

6. Apr 18, 2014

### ghostops

yeah I see it now

so starting my from my mistake
m=-s'/s=-s'/(f-s') = (-s'/f)-(s'/-s)'
m = -s'/f+1

m = -s'/f+1
m-1=-s'/f
fm+-f=-s'
-fm+f=s'

1/s-1/fm+f=1/f
1/s=1/f+1/fm-f
1/s = 1/f + 1/fm -1/f
s=(fm)^-1

Last edited: Apr 18, 2014
7. Apr 18, 2014

### Staff: Mentor

No, the part that I put in red isn't true. What you're trying to do here is similar to 1/(a-b) = 1/a - 1/b, which doesn't work. (Try it with a numerical example if you need to convince yourself.)

8. Apr 18, 2014

### dauto

how did you go from -fm+f=s'
to 1/s-1/fm+f=1/f ?

You 're making too many silly algebra mistakes. You need more practice.