Discover the Focal Length of a Convex Mirror Using Object and Image Distance

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To find the focal length of a convex mirror, the relationship between object distance, image distance, and focal length is used, expressed as 1/f = -(image distance) / (object distance). Given an object height of 30 cm placed 20 cm in front of the mirror and an image height of +10 cm, the magnification can be calculated as the ratio of image height to object height. This magnification also relates to the distances: magnification = - (image distance) / (object distance). By determining the image distance from the magnification and substituting it back into the focal length equation, the focal length can be calculated. Understanding these relationships is crucial for solving the problem effectively.
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Convex mirror. PLEASE HELP!

Homework Statement



An object 30 cm tall is placed 20 cm in front of a convex mirror. If the height of the image is +10 cm, find the focal length of the mirror.

Homework Equations





The Attempt at a Solution



I know to use 1/f = -(Image distance from V) / Object distance from V. But, now they tell me how tall they are. How to solve now?
 
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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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