This isn’t a homework problem, but my daughter is preparing for a science competition. She got assigned questions about microbiology - not her choice.
So, if I may ask, how would you solve this?
A cell is observed to take up about half the field of view at 4x magnification (under a light microscope). What is the length of the organism?
Is there really enough info here to answer the question? And, if so, please explain the approach.
Are you sure its a 4X magnification? Remember, you must multiply the magnification of both your viewing lens and the objective lens. More likely, your magnification is 4 X ?, where ? is your eyepiece magnification.
First place a clear plastic ruler on the stage and measure the field diameter in millimeters. Next, estimate the number of cells that fit across a field, as you already have done. Do a little math and you have your cell size.
Keep in mind that a really big plant cell will be about 0.2 mm while a really big animal cell might be 0.05 mm.
If that is truly all the information you have been given, then clearly it is unanswerable. Are you sure, however, that there is not some other relevant information (e.g., about the size of the field of view) elsewhere in the assignment?