Physics quiz question: focal length of microscope objective lens

Physics 205B Quiz 2, spring semester 2017
Cuesta College, San Luis Obispo, CA

A Leitz Ortholux microscope[*] (–47× magnification) has an eyepiece lens with a focal length of +1.8 cm, and a 17.0 cm distance between the objective and eyepiece. The focal length of the objective lens is:
(A) +0.53 cm.
(B) +4.5 cm.
(C) +15.2 cm.
(D) +85 cm.

[*] microscopy-uk.org.uk/mag/artnov15/The%20Mechanical%20Tube%20Length%20Version%201.pdf.

Correct answer (highlight to unhide): (B)

The angular magnification M of a microscope is given by:

M = –(L – f_e)·N/(f_o·f_e),

where L is the distance between the objective and eyepiece, N = 25 cm is the nominal value for the near point, and f_o and f_e are the focal lengths of the objective and eyepiece, respectively. Thus with the given values given in the statement of the problem, the focal length of the objective can be solved for:

f_o = –(L – f_e)·N/(M·f_e),

f_o = –(17.0 cm – 1.8 cm)·(25 cm)/((–47)·(1.8 cm)),

f_o = +4.4917257683 cm,

or to two significant figures, the focal length of the objective is +4.5 cm.

(Response (A) is N/M; response (C) is L – f_e; response (D) is M·f_e.)

Sections 30882, 30883
Exam code: quiz02J4sZ
(A) : 1 student
(B) : 21 students
(C) : 5 students
(D) : 3 students

Success level: 70%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.43