Physics quiz question: refocusing a telescope after switching eyepiece

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

"Telescope at Lick Observatory"
James (supermuch)
flic.kr/p/9zsu4Q

The Lick Observatory telescope[*] has a 1,763 cm focal length objective lens with a 3.2 cm focal length eyepiece. This eyepiece is then replaced by a 1.6 cm focal length eyepiece. As a result of replacing eyepieces, the distance between the objective lens and the eyepiece must __________ for the telescope to remain in focus.
(A) increase.
(B) remain the same.
(C) decrease.
(D) (Not enough information given.)

[*] mthamilton.ucolick.org/techdocs/telescopes/36inch/intro/.

Correct answer (highlight to unhide): (C)

The distance between the objective lens and eyepiece for a telescope (focused on a distant object) is merely the sum the of the objective lens focal length f_o and the eyepiece focal length f_e, which originally was:

f_o + f_e = 1,763 cm + 3.2 cm = 1,766 cm.

Then replacing the eyepiece with shorter 1.6 cm focal length lens (which would increase its angular magnification) would result in a shorter distance between the objective lens and eyepiece:

f_o + f_e = 1,763 cm + 1.6 cm = 1,765 cm.

Thus the length of the telescope must be shortened by approximately 1 cm in order to remain in focus.

(The reason why the distance between the objective lens and eyepiece for a telescope is merely the sum of the objective lens and eyepiece focal lengths can be seen from the above telescope ray tracing, where the object to the far left is extremely distant, such that its rays are essentially parallel. The objective lens then focuses these parallel light rays onto an intermediate real image located at its focal point F_o. Then this real image becomes an object for the eyepiece, where it is placed on the focal point F_e in front of the eyepiece to maximize its angular magnification.

Since the intermediate real image is located a distance of f_o from the objective lens, and a distance of f_e from the eyepiece, then the total distance from the objective lens to the eyepiece is just f_o + f_e.)

Student responses
Sections 30882, 30883
Exam code: quiz02f3MA
(A) : 9 student
(B) : 3 students
(C) : 29 students
(D) : 0 students

Success level: 71%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.50