Finding height of image for a concave mirror

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To find the height of an image (hi) for a concave mirror, the magnification equation m = -di/do = hi/ho is essential. The focal length (f), object distance (do), and image distance (di) are known, but the height of the object (ho) is required to calculate hi. Without the height of the object, it is impossible to determine the height of the image since the magnification relies on this value. The relationship between distances and heights is fixed, and arbitrary choices for image distance cannot be made. Therefore, the height of the object is necessary to solve for the height of the image.
chester89
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Ok, there's something I just don't understand. I know that to find the height of an image (hi), you need to use the magnification equation m = -di/do = hi/ho. And for this question, the focal length (f), distance of object (do), and distance of image (di) are given. Now, if I want to find the height of the image (hi), I would need the height of the object (ho) to finish the equation, but I don't, so now I'm stumpted on what to do with this question.

I know 'hi = -diho/do' is the equation but if I don't have ho, than how can I find hi.

Any help would be greatly appreciated.
 
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Edited, misinterpretation.

I don't believe you can find the height of the image without the height of the object. The focal length and a given object distance will determind the image distance. No other focused distance is possible. We cannot arbitrarily choose some image distance.
 
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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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