Solving for Magnification in a Microscope

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The discussion revolves around calculating the magnification of a microscope constructed from two lenses with focal lengths of 2.8 cm and 1.1 cm. The more powerful lens, with a focal length of 1.1 cm, is used as the objective, and the distance between the objective and eyepiece is set at 15 cm. The user calculates the object distance (s) as 1.2 cm and the image distance (s') as 13.2 cm, yielding an objective magnification of -11. However, confusion arises regarding the correct formula for the eyepiece magnification and how to combine both magnifications for the final result. Despite following the book's logic for different numerical values, the user finds discrepancies in their calculations, leading to frustration.
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1. Your task in physics laboratory is to make a microscope from two lenses. One lens has a focal length of 2.8 cm, the other 1.1 cm. You plan to use the more powerful lens as the objective, and you want the eyepiece to be 15 cm from the objective.

What is the magnification of your microscope?




2. Thin lens equation
M_obj = -s'/s
M_eye = ?




3. In part one I solved for s, and s = 1.2cm. The more powerful lens is the one with f = 1.1, and s' = 13.2. Thus, the magnification of the objective lens should be -s'/s = -13.2/1.2 = -11. Is that correct? Also, what do I sue for the magnification of the eye? I know that I have to mutiply those two values to obtain my final answer.
 
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This one's really killing me guys. I think I've got all my sign conventions right, and none of the incorrect answers I've tried have said, "check your signs." I've tried the s'=15cm for the image distance (which I used to calculate s in part one, which was correct...) but that didn't work, i.e. -(15/1.1)(25/2.8). I also tried using s'=15-2.8=12.2, putting the image from the objective projected onto the focal point of the eyepiece.

wtf...
 
The answer is in the back of the book, but with different numerical values. I worked out how to get the correct answer for the book numbers, then applied the exact same logic to the question with the values I am asking about... and it says it's wrong...
 
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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