Object distance and magnifiation

[996gt2]

Homework Statement

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

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

Homework Equations

m_obj=-L/f_obj

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!

 

[996gt2]

Anyone?

 

[Redbelly98]

Check out two of the equations here:
https://www.physicsforums.com/library.php?do=view_item&itemid=148

You need the Gaussian lens formula, as well as the expression for magnification m given there.

 

[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?

 

[Redbelly98]

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

 

[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 :)