You are tasked with making a microscope with a magnification of 1000 using a converging lens with
a focal distance of 1.5 cm for the objective. The tube length given to you is 30 cm long. What
should the focal distance of the eyepiece be if you want the eyes to be relaxed while observing with
this microscope? Assume a near point of 25 cm.

Question

You are tasked with making a microscope with a magnification of 1000 using a converging lens with 
a focal distance of 1.5 cm for the objective.   The tube length given to you is 30 cm long.  What 
should the focal distance of the eyepiece be if you want the eyes to be relaxed while observing with 
this microscope?  Assume a near point of 25 cm.

anonymous · Answer

For compound microscope:
If you want the eye to be relaxed then 
magnification of the miocroscope=(Vo/Uo)(D/fe)
i.e (Vo/Uo)(D/fe)=1000.....(1)
and for objective lens : apply lens formula
                          1/Vo-1/Uo=i/fo
						  1-Vo/U0=Vo/fo
						  Vo/Uo=1-Vo/fo...(2)
						  from (1) and (2)
						  we get....
						   (1-Vo/fo)(D/fe)=1000....(3)
						    since length of the tube is 30cm then 
							          Vo+fe=30 cm....(4)
									   from (3)and (4), get the value of fe......