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It is an optical instrument used for observing highly magnified images of tiny objects.
O - Objective
E - EyepieceD - Distance of distinct vision
AB - ObjectA'B' - First image
A"B" - Final imageO1,O2 - are optic centers of O and E
O, FO - Focal length of objectiveO, Fe - Focal length of eyepiece
Magnifying power of compound microscope is defined as the ratio of the angle subtended at the eye by the final image to the angle subtended at the eye by the object, when both the final image and the object are situated at the least distance of distant vision from the eye.

m = magnification produced x magnification produced due to eye lens due to objective lens
m = me x mo

(-ve sign shows that final image is inverted with respect to the object)
Note:
If the object is very close to fo, the focus of lens O then

Vo = OlBl O1O2 = L = length of tube
If fo and fe both are small then magnifying power will be large. 


