Object distance and magnifiation

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To achieve a lateral magnification of -40 with a microscope objective of 9mm focal length, the object distance must be calculated using the Gaussian lens formula. The initial calculation of 360mm was incorrect, as the object distance should be much closer to the focal length. The correct object distance is approximately 9.225mm, derived from the formula 1/f = 1/s + 1/s'. Using adapted formulas from textbooks can lead to inaccuracies in such scenarios. The discussion emphasizes the importance of applying the correct optical principles for precise calculations.
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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



mobj=-L/fobj

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!
 
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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\approxf. Similarly, the focal length of the objective is much less than the length of the microscope tube, so s'\approxL

Is it wrong to use these adapted formulas from the book?
 
Yes, the object distance will be close to f=9mm. So your answer of 360mm is way way off.
 
Hmmm, after some thinking I got:

1/f=1/s+1/s'
1/9mm=1/x+1/40x
x=9.225mm<br />

And it was right! Thanks for the suggestion to use the Gaussian optics formulas :)
 
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Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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