How long is the image of the meter stick?

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The discussion revolves around determining the length of the image of a meter stick when placed in front of a concave mirror. Using the mirror equation, the image distances for both ends of the meter stick are calculated as 120 cm and 53.3 cm. The length of the image is then derived by finding the difference between these two distances. This leads to two potential lengths: 173.3 cm or 66.7 cm, depending on whether the distances are added or subtracted. The correct approach emphasizes that the length of the image corresponds to the difference in the positions of each end.
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Homework Statement



The figure shows a meter stick held lengthwise along the optical axis of a concave mirror. (Intro 1 figure) - figure attached

How long is the image of the meter stick?

Homework Equations



1/f = 1/do + 1/di

3. The Attempt at a Solution [/b

1/di = 1/f - 1/do = 1/40 -1/60
di = 120 cm

but I am not sure how to proceed after this part

any help would be appreciated
 

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You found the location of the image of one end of the stick; now find the other.
 
so for the second point
1/di = 1/f - 1/do = 1/40 - 1/160
di = 53.3

so the length of the scale would be (120+53.3) = 173.3 cm

or (120-53.3) = 66.7 cm ?
 
The length of the image will be the difference in the position of each end.
 
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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