Physics midterm problem: bifocal prescription

Physics 205B Midterm 1, spring semester 2011
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 24.24

"Image of an eyeglass prescription"
Dpbsmith

http://en.wikipedia.org/wiki/File:Specrx-prescription2.jpg

Shown above is an (edited) copy of an eyeglass prescription, where the far and near corrective optics are prescribed to be –3.25 diopters and +2.00 diopters, respectively, for the right and left eyes. Determine (a) the uncorrected far point for the right eye, and (b) the uncorrected near point for the left eye of this patient. (Neglect the distance between these glasses and eyes.) Show your and explain your reasoning using properties of lenses and vision.

Solution and grading rubric:

• p:
  Correct. Uses the thin lens equation 1/p + 1/q = 1/f = P, where p is the far point F or near point N, and q = –∞ or –0.25 m, respectively, and solves for F and N. Minor negative sign errors okay.
  
• r:
  Nearly correct, but includes minor math errors.
  
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Applies F = –1/D correctly to find far point, but incorrectly applies N = 1/P to find near point; or may use N = 1/(P – 1/(0.25 m)) correctly to find near point, but incorrectly applies it to find the far point.
  
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner.
  
• x:
  Implementation of ideas, but credit given for effort rather than merit.
  
• y:
  Irrelevant discussion/effectively blank.
  
• z:
  Blank.
  

Grading distribution:
Section 30882
Exam code: midterm01g74S
p: 1 student
r: 0 students
t: 7 students
v: 0 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 2180) with a relatively minor sign error: