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a) Design a microscope with a tube length $\ell = 10$ cm and a magnification of 500. Draw it below to scale. Derive its magnification in terms of $f_o$ (the objective lens) , $f_e$, $\ell$, and any other parameters you think necessary. You may pick $f_o$ and $f_e$ to have any ``sensible'' values, and can make the microscope invert the image or not as you wish.

b) Determine where (that is, the actual position in cm) one has to place the object in front of the objective lens in order for the relaxed, normal eye to view its image at infinity through the eyepiece. Note that this answer will depend (obviously) on $f_o$ and other parameters, so the number answer is less important than the algebra (which is what will be checked).