The focal lengths of the objective lens and the eyepiece in a microscope are 2.90 mm and 2.50 cm,respectively.An object is placed 3.00 mm from the objective.The image of this object is viewed with the eyepiece adjusted for minimum eyestrain for persons with a near point of 25 cm.What is the distance between the objective and the eyepiece?
A)9.9 cm
B)9.0 cm
C)15 cm
D)11 cm
E)13 cm

Question

Quizplus · Accepted Answer

Using the thin lens equation, we can calculate the distance between the objective lens and the image produced by it:
(1/f_objective) = (1/do) + (1/di)
where f_objective is the focal length of the objective lens, do is the object distance (3.00 mm), and di is the image distance.
Solving for di, we get:
di = 1 / (1/f_objective - 1/do)
di = 2.872 mm (image distance)
Now, using the angular magnification equation, we can find the distance between the objective and the eyepiece:
M = fo/fe * (di / (do + fo))
where fo and fe are the focal lengths of the objective and eyepiece, respectively.
Solving for do + fo, we get:
(do + fo) = di / (M * (fo/fe))
Substituting the given values, we get:
(do + fo) = 12.64 cm
Finally, since the image produced by the objective is located do + fo away from the eyepiece, the distance between the objective and the eyepiece is:
(do + fo) - di
= 11.0 mm
= 1.1 cm
= 11 cm (rounded to one decimal place)

The Focal Lengths of the Objective Lens and the Eyepiece