Astronomy midterm question: high magnification, low resolution telescope

Astronomy 210 Midterm 1, fall semester 2011
Cuesta College, San Luis Obispo, CA

[20 points.] An editorial on a online web mapping and travel guide service(*) gave the following advice on purchasing a telescope:

The cheap telescopes found in toy stores all too often will have magnification as the main [selling] point... In fact [when] a telescope is advertised with the main [selling] point being its magnification...it is likely not going to show you any kind of details [like] those pictures on the box!

Discuss how it is possible for a telescope to have lots of magnification but not be able to show fine details. Support your answer using the properties of telescope parameters and telescope powers.

*Source: Successu7, "Top Mistakes Made When Buying a First Telescope for Home," 
http://www.streetdirectory.com/travel_guide/153773/science/top_mistakes_made_when_buying_a_first_telescope_for_home.html.

Solution and grading rubric:

• p = 20/20:
  Correct. The focal length of the primary lens/mirror and eyepiece determines the magnification, while diameter of primary lens/mirror determines the (light-gathering power and) resolving power. Since resolving power and magnification depend on different parameters, then it possible for the telescope to have a high f_primary/f_eyepiece ratio (and thus high magnification), but small diameter (and thus poor resolution).
  
• r = 16/20:
  Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. Discusses what parameters one of the powers (magnifying or resolving) depends on, but only implies that the other power depends on a different parameter.
  
• t = 12/20:
  Contains right ideas, but discussion is unclear/incomplete or contains major errors. Distinguishes between image qualities affected by magnification (size) and resolution (detail), and how an image could be large and coarse, but does not connect this to the focal length and diameter properties of telescopes.
  
• v = 8/20:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner.
  
• x = 4/20:
  Implementation/application of ideas, but credit given for effort rather than merit.
  
• y = 2/20:
  Irrelevant discussion/effectively blank.
  
• z = 0/20:
  Blank.
  

Grading distribution:
Section 70158
Exam code: midterm01sg5U
p: 5 students
r: 9 students
t: 21 students
v: 1 student
x: 1 student
y: 0 students
z: 0 students

Section 70160
Exam code: midterm01nH3d
p: 9 students
r: 9 students
t: 10 students
v: 0 students
x: 1 student
y: 1 student
z: 0 students

A sample "p" response (from student 8436):

A sample "p" response (from student 0816):