A crude symmetric hand held microscope consists of two converging lenses each of

Question

A crude symmetric hand held microscope consists of two converging lenses each of focal length 5.0 cm fastened in the ends of a tube 40 cm long. What is the overall angular magnification of the microscope? (Use a near point of 25 cm.)
Select one:
a. -1
b. -40
c. -30
d. 40
e. -5

A crude symmetric hand held microscope consists of two converging lenses each of focal length 5.0 cm fastened in the ends of a tube 40 cm long. How far from the objective should the object be placed? (Use a near point of 25 cm.)
Select one:
a. 5.83 cm
b. 5 cm
c. 40 cm
d. 5.71 cm
e. It doesn't matter.

For the first one, the answer is -30 but using the equation of the overall angular magnification of the microscope shouldn't it be -40?I don't know how to do the second one.

Explanation / Answer

For Objective Focal Length -
Forcing the final image to be at infinity requires the real image formed by the objective to be at the focal length of the eyepiece.This means that the image distance for the objective is the tube length minus the eyepiece focal length.

di = 40 - 5 = 35 cm

1/f = 1/di + 1/do
1/5 = 1/35 + 1/do
do = 35/6

Mo = -di/do
Mo = - 35/(35/6)
Mo = - 6

For Eyepiece -
Me = 25/fe
Me = 25/5
Me = 5

Total Magnification, M = Mo * Me =
M = 5*-6
M = -30

(b)
Above we calculated the Distance of object from 1st Objective Lens, do = 35/6 cm
do = 5.83 cm

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