Maximum Magnification of Microscope

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To determine the maximum magnification of a compound microscope with a 0.70 cm objective lens and a 5.0 cm eyepiece lens mounted 18 cm apart, the relevant formula for angular magnification is M=(25/f_e)(l-f_e/d_o). The discussion highlights that magnification increases as the object distance (d_o) decreases, suggesting that theoretically, magnification could approach infinity. However, the calculated maximum magnification is stated to be 130, indicating a practical limit based on the configuration of the lenses. The conversation emphasizes the need to consider the minimum object distance to accurately assess maximum magnification. Understanding these parameters is crucial for solving the problem effectively.
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Homework Statement


You are building a compound microscope with an objective lens of focal length 0.70 cm and an eyepiece lens of focal length 5.0 cm. You mount the lenses 18 cm apart. What is the maximum magnification of your microscope?


Homework Equations


M=\left(\frac{25}{f_e}\right)\left(\frac{l-f_e}{d_o}\right)

The Attempt at a Solution


I tried using the above formula for overall angular magnification and got $\frac{65}{d_o}$ and so the magnification depends on $d_o$, and the smaller $d_o$ gets the larger the magnification. However it looks like the largest magnification is \infty, but the answer is 130. How do you do this problem?
 
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Does anybody know how to approach this problem?
 
I feel like there is no maximum magnification unless there is a minimum distance the object can be placed to the objective lens.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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