Physics midterm problem: object distance with greatest magnification

Physics 205B Midterm 1, spring semester 2015
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 23.63

An object can be placed either 16 cm or 14 cm in front of a f = +15 cm converging lens. Decide which object distance will result in the largest image (regardless of being real/virtual, or inverted/upright), or if there will be a tie. Show your work and explain your reasoning using the properties of lenses, thin lens equations and/or ray tracings.

Solution and grading rubric:

• p:
  Correct. Compares the linear magnification ratios of both object distances using one of two methods:
  1. determines the image distances produced by these objects, then sets up the ratio m = –d_i/d_o to find their respective linear magnification factors;
  2. a carefully, properly scaled ray tracing diagram.
• r:
  Nearly correct, but includes minor math errors. May have sign errors or inverse errors.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least enough steps are shown that would theoretically result in a complete answer, multiple errors (or omission of last step of finding m = –d_i/d_o ratio) notwithstanding. May draw a ray tracing diagram that does not have its object distances properly scaled with regards to the focal points, but at least makes a consistent conclusion based on the faulty scaling of object positions.
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Ray tracings have real images for both cases, etc.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 30882, 30883
Exam code: midterm01p34K
p: 21 students
r: 6 students
t: 13 students
v: 6 students
x: 1 student
y: 0 students
z: 0 student

A sample "p" response (from student 8984):