Physics quiz question: microscope objective lens focal length

Physics 205B Quiz 2, spring semester 2014
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 24.37

The Richter Optica F1 microscope[*] (–40× magnification) has an eyepiece lens with a focal length of +2.5 cm, and a tube length (measured from focal point to focal point) of approximately 25 cm. The focal length of the objective lens is:
(A) +0.63 cm.
(B) +1.6 cm.
(C) +6.3 cm.
(D) +100 cm.

[*] microscopeworld.com/p-1735-richter-optica-f1-elementary-microscope.aspx.

Correct answer (highlight to unhide): (C)

The angular magnification M of a microscope is given by:

M = –(L·N)/(f_o·f_e),

where the "tube length" (the focal point to focal point distance) L is given as 25 cm, the nominal near point N is 25 cm, and the eyepiece focal length is f_e is also given as +2.5 cm. Thus the objective focal length is:

f_o = –(L·N)/(M·f_e) = +6.3 cm.

Response (A) is N/M; response (B) is M/N; and response (D) is M·f_e.

Sections 30882, 30883
Exam code: quiz02O8Jt
(A) : 4 students
(B) : 7 students
(C) : 25 students
(D) : 5 students

Success level: 60%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.48