The distance between the lenses in a compound microscope is 18 cm. the focal length of the objective is 1.5 cm. if the microscope is to provide an angular magnification of -67 when used by a person with a normal near point (25 cm from the eye), what must be the focal length of the eyepiece?

The correct answer is 3.58 cm.

Explanation:

For a compound microscope where the object is placed very close to the focal point of the objective, it is found that the angular momentum is given by:  

m = - ( L - fe) N / fo *fe

m = - (18 - fe) (25) / 1.5 * fe

It is given that m = -67

so, 67 = (18-fe) (25) / 1.5 * fe

100.5 fe = 450 - 25 fe

125.5 fe = 450

fe = 450 / 125.5

fe = 3.58 cm

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