Calculating Magnification of a Microscope: Solving the Magnification Problem

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To calculate the magnification of a microscope, the user initially attempted to apply the lens formula but found it unhelpful. They then shifted to using the magnification formula M = hi ÷ ho = -di ÷ do. The object height is 4.00 x 10^-7 m, and the image height is 1.00 x 10^-4 m, leading to a magnification calculation of M = (1.00 x 10^-4) ÷ (4.00 x 10^-7), which simplifies to 250. The user is seeking guidance to confirm their calculations and complete multiple similar problems.
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A microscope produces an image that is 1.00 x 10-4 m high from an object that is 4.00 x 10-7m high. What is the magnification of the microscope?



I've already tried applying this with the formula 1f = 1÷do + 1÷di

So: 1f = ( 1÷ 4.00 x 10-7) + ( 1÷ 1.00 x 10-4 )
1f = 250 000 + 1000
1f ÷ 1 = 251 000 ÷ 1
f = 251 000

Already, this doesn't seem to be the right answer in my opinion.. but I'm not sure. Now, I'm trying to use the formula M = hi ÷ ho = -di ÷ do

Can anyone help sort of.. guide me in the right direction on how I'm supposed to solve this now? (= ~Thanks
 
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Three hours of no replies.. I'm sorry for being impatient but I have around 20 of these questions to solve for tomorrow.. so yeah ._. Help please?
 
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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