Physics quiz question: focal length of microscope eyepiece

Physics 205B Quiz 2, spring semester 2016
Cuesta College, San Luis Obispo, CA

A Newport "M-10X" objective lens[*] has a 1.65 cm focal length, and is used in a microscope with a 16.0 cm distance between the objective and eyepiece. To obtain an angular magnification of –150×, a __________ focal length eyepiece must be used.
(A) 1.10×10^–2 cm.
(B) 1.5 cm.
(C) 1.8 cm.
(D) 14.4 cm.

[*] search.newport.com/?x1=sku&q1=M-10X.

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 eyepiece can be solved for:

Mf_o·f_e = –(L – f_e)·N,

Mf_o·f_e = –L·N + f_e·N,

Mf_o·f_e – f_e·N = –L·N,

f_e·(M·f_o – N) = –L·N,

f_e = L·N/(N – M·f_o),

f_e = (16.0 cm)·(25.0 cm)/((25.0 cm) – (–150)·(1.65 cm)),

f_e = 1.46788990826... cm,

or to two significant figures, the focal length of the eyepiece is 1.5 cm.

(Response (A) is f_o/M; response (C) is where the above calculation uses M = +150 in the denominator; response (D) is L – f_o.)

Sections 30882, 30883
Exam code: quiz02f3MA
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