Astronomy clicker question: light-gathering power

Astronomy 210, Fall Semester 2008
Cuesta College, San Luis Obispo, CA

Students were asked the following clicker question (Classroom Performance System, einstruction.com) at the start of their learning cycle:

An optical refractor telescope, and an optical Schmidt-Cassegrain reflector telescope, both have tubes 15 cm in diameter and 1.5 m in length, and use identical eyepieces. Which telescope has the greater light-gathering power?
(A) The refractor.
(B) The reflector.
(C) (There is a tie.)
(D) (More information is needed to determine this.)
(E) (I'm lost, and don't know how to answer this.)

Section 70160
(A) : 6 students
(B) : 6 students
(C) : 9 students
(D) : 1 student
(E) : 0 students
(F) : 0 students

This question was asked again after displaying the tallied results with the lack of consensus, with the following results. No comments were made by the instructor, in order to see if students were going to be able to discuss and determine the correct answer among themselves.

Section 70160
(A) : 10 students
(B) : 2 students
(C) : 16 students
(D) : 0 students
(E) : 0 students
(F) : 1 student

Correct answer: (C) or (A)?

Both telescopes have the same diameter, and thus the same area when calculated from pi*(diameter/2)^2. However, the reflector will have a secondary mirror that will block some of the area that will receive incoming light, and so it will have slightly less LGP than the refractor.

Pre- to post- peer-interaction gains:
pre-interaction correct = 27% (A) + 41% (C)
post-interaction correct = 34% (A) + 55% (C)
Hake (normalized) gain <g> = 67% (with both (A) and (C) considered "correct" choices)