Astronomy midterm question: purchasing a wider or longer telescope?

Astronomy 210 Midterm 1, fall semester 2015
Cuesta College, San Luis Obispo, CA

An astronomy question on an online discussion board[*] was asked and answered:

??: To replace my telescope with a better one, should I buy one with a tube longer than the one I already have, or one with a diameter wider than the one I already have?
GG: First priority would be to buy a wider diameter telescope instead of one that is longer.

Discuss why this response is correct. Support your answer using the properties of telescopes and telescope powers.

[*] answers.yahoo.com/question/index?qid=20150925205424AARw53Z

Solution and grading rubric:

• p:
  Correct. Discusses how area and diameter of a telescope's primary mirror or lens respectively determines the light-gathering power and resolving power, such that a "wider" diameter telescope would be better to make fainter objects brighter, and allow finer details to be seen; and while the "longer" telescope would have a longer primary mirror/lens focal length and thus better magnification, but this would be a lower priority after improving a telescope's ability to make faint objects with fine details visible.
• r:
  Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. Correct and complete discussion of two of the three telescope parameters and powers.
• t:
  Contains right ideas, but discussion is unclear/incomplete or contains major errors. Problems with either diagram or discussion. Discussion of only one of the three telescope parameters and powers is correct and complete.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. Misconceptions or non-relevant concepts.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Section 70160
Exam code: midterm01nW6b
p: 3 students
r: 2 students
t: 15 students
v: 9 students
x: 1 student
y: 1 student
z: 0 students

A sample "p" response (from student 4338):