Acompound microscope operated in near point adjustment comprises an objective lens of focal length 5.0 cm and an eyepiece lens of focal length 12.0 cm. if the near-point distance is 25.0 cm, and the overall magnification of the microscope is required to be 12.0 x, how far apart must the lenses be placed?

28.8 cm

Explanation:

Magnification in a microscope is:

M = Mo * Me

Where

Mo: magnification of the objective,

Me: Magnification of the eyepiece.

The magnification of the objective if:

Me = npd/fe

Where:

npd: near point distance

fe: focal length of the eyepiece

The magnification of the objective:

Mo = d/fo

Where

d: the distance between lenses

fo: focal length of the objective

Then

M = npd/fe * d/fo

d = M * fe * fo / npd

d = 12 * 5 * 12 / 25 = 28.8 cm