A compound microscope consists of a 15X eyepiece and a 10X objective, and has a

Question

A compound microscope consists of a 15X eyepiece and a 10X objective, and has a standard tube length L = 160 mm. The microscope is designed for a user with normal vision, i.e. with a near point of 25 cm.

The microscope is used to image a cell of size 4.9 µm.

A) Calculate the total angular magnification of the microscope.

B) What is the focal length of the eyepiece?

C) What is the focal length of the objective?

D) What would the angular size of the cell, unaided, be in radians if viewed with the unaided eye from a near-point distance?

E) What is the angular size of the cell as viewed through the microscope aided, in radians?

Explanation / Answer

(A)
Total Angular Magnification = Magnification of the eye piece * Magnification of the Objective
Total Angular Magnification = 15 * 10
Total Angular Magnification = 150 x

(B)
Focal Length of Eye piece,
Me = 25/fe
fe = 25/15
fe = 1.67 cm

(C)
Focal Length of the objective,
Mo = - L/fo
fo = - 160 * 10^-1 / 10
fo = -1.6 cm

(D)

unaided = ho/N
unaided = (4.9 * 10^-6) / (25 * 10^-2)
unaided = 1.96 * 10^-5 rad

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