Lenses - Thin-Lens Equation and Magnification Equation

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The discussion revolves around solving a homework problem involving the thin-lens equation and magnification for two camera lenses with focal lengths of 35.0 mm and 150.0 mm. The user initially struggles with calculating the image height of a woman standing 9.00 m from the camera, using the formula for image distance and magnification. After attempting the calculations, they realize a unit conversion error, mistaking 35 mm for 0.035 m instead of the correct value. The importance of careful unit conversion is emphasized, as it significantly impacts the accuracy of the results. The thread concludes with a reminder to double-check units in physics problems.
missmia
[SOLVED] Lenses - Thin-Lens Equation and Magnification Equation

I can't figure out what I am doing wrong, your help would be greatly appreciated :)

Here is the Homework Problem

A camera is supplied with two interchangeable lenses, whose focal lengths are 35.0 and 150.0 mm. A woman whose height is 1.80 m stands 9.00 m in front of the camera. What is the height (including sign) of her image on the film, as produced by each of the following.
(a) the 35.0 mm lens
(b) the 150.0 mm lens

ATTEMPTED SOLUTION:

\frac{1}{d_{i}} = \frac{1}{.0035m} - \frac{1}{9.0m}

which gives d_{i} = .003501m

then, I used the magnification equation: m = - \left[\frac{.003501m}{9.0m}\right] = -3.89 x 10^{-4}x

then, I used h_{i} = mh_{o} = -3.89 x 10^{-4} x 1.80m = -7.00 x 10^{-4}

But, the answer that I got is incorrect! Please Help! Thank you!
 
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Be careful with the units. remember 35mm is 3.5cm which is 0.035m.
 
oh gosh! I can't believe I didn't notice that. Thanks again :)
 
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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