# Object distance and magnifiation

1. Feb 4, 2009

### 996gt2

1. The problem statement, all variables and given/known data

A 6mm diameter microscope objective has focal length 9mm.

What object distance is required to achieve a lateral magnification of -40?

2. Relevant equations

mobj=-L/fobj

3. The attempt at a solution

-40x=-L/9mm

L=360mm

Why isn't the answer 360mm? I think it might have something to do with the diameter of the lens, but I'm not completely sure. Can someone explain? Thanks!

2. Feb 5, 2009

Anyone?

3. Feb 5, 2009

### Redbelly98

Staff Emeritus
4. Feb 5, 2009

### 996gt2

Well, the formula I included is basically an approximation derived from the Gaussian lens formula...at least, that's how my book put it.

Basically, with a microscope, the object is very very close to the focal point, so s$$\approx$$f. Similarly, the focal length of the objective is much less than the length of the microscope tube, so s'$$\approx$$L

Is it wrong to use these adapted formulas from the book?

5. Feb 5, 2009

### Redbelly98

Staff Emeritus
Yes, the object distance will be close to f=9mm. So your answer of 360mm is way way off.

6. Feb 5, 2009

### 996gt2

Hmmm, after some thinking I got:

$$1/f=1/s+1/s'$$
$$1/9mm=1/x+1/40x$$
$$x=9.225mm$$

And it was right! Thanks for the suggestion to use the Gaussian optics formulas :)