A compound microscope consists of a 20X eyepiece and a 100X objective, and has a

Question

A compound microscope consists of a 20X eyepiece and a 100X 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 2.7 µm.

a) Calculate the total angular magnification of the microscope.

b) What is the focal length of the eyepiece? __cm

c) What is the focal length of the objective? __cm

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

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

Explanation / Answer

(a)
Total Angular Magnification of Compound Microscope, = Mo*Me
Where,
Mo is Magnification of objective lens.
Me is Magnification of eyepiece.

M = 20 * 100
M = 2000

(b)
Me = 25/fe
fe = 25/Me
fe = 25/20
fe = 1.25 cm

(c)
Mo = l/fo
fo = l/Mo
fo = 160 / 100
fo = 1.6 mm
fo = 0.16 cm

(d)
sin() = (2.7 * 10^-6)/(0.25)
unaided = 1.08 * 10^-5 rad

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