A custom-made compound microscope (see the figure below) with an objective lens

Question

A custom-made compound microscope (see the figure below) with an objective lens with a focal length of 3.75 cm, an eyepiece lens with a focal length of 6.35 cm and a barrel length of 25.5 cm is used to view a 0.100 cm specimen mounted on a microscope slide. Since the microscope is custom-made, it varies slightly from a standard production microscope in that the object distance for the objective is so much larger than the focal length of the objective that we cannot set the object distance for the objective equal to the focal length of the objective. However, the image formed by the objective is close enough to the focal point of the eyepiece that we are justified in setting the object distance for the eyepiece equal to the focal length of the eyepiece. Finally, the microscope is being used by a lab technician with a near point of 34.5 cm. (Use the exact values you enter to make later calculations.)

a) distance the specimen (object) is mounted from the objective lens (Enter your answer to at least two decimal places.) in centimeters

b)  magnification of the objective lens (Include the sign of the value in your answer. Enter your answer to at least two decimal places.)

c)  magnification of the eyepiece lens (Include the sign of the value in your answer.)

d) overall magnification for the microscope (Include the sign of the value in your answer.)

Explanation / Answer

Objective Lens Focal Length, f1 = 3.75 cm
Eyepiece Lens Focal Length, f2 = 6.35 cm
Barrel Length L = 25.5 cm
(a)
Distance of Image formed by Objective lens = L - f2 = 25.5 - 6.35 cm
di1 = 19.15 cm

1/f1 = 1/di1 + 1/do1
1/3.75 = 1/19.15 + 1/do1
do1 = 4.66 cm
Distance the specimen (object) is mounted from the objective lens , do1 = 4.66 cm

(b)
M = -di/do
M = - 19.15/4.66
Mo = - 4.11
Magnification of the objective lens, Mo = -4.11

(c)
M = -di/do
M = - (-34.5) / 6.35
Me = 5.43
Magnification of the eyepiece lens , Me = 5.43

(d)
Overall Magnifiation of Microscope, M = Mo*Me
M = -4.11* 5.43
M =  -22.32
Overall Magnifiation of Microscope, M =  -22.32

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