Physics midterm question: objects at diverging lens focal points

Physics 205B Midterm 1, spring semester 2013
Cuesta College, San Luis Obispo, CA

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

Two diverging lenses available from a commercial optics supplier have focal length f = –6 cm and f = –9 cm, respectively[*]. An object placed 6 cm in front of the 
f = –6 cm lens creates an image. This same object placed 9 cm in front of the f = –9 cm lens also creates an image. Discuss why these images will have the same size. Explain your reasoning by using the properties of lenses, thin lens equations and/or ray tracings.

[*] edmundoptics.com/optics/optical-lenses/double-concave-dcv-spherical-singlet-lenses/uncoated-double-concave-dcv-lenses/1756.

Solution and grading rubric:
  • p:
    Correct. Uses ray diagram and/or thin lens equation(s) to explain why the virtual images produced by objects placed at the focal points of diverging lenses must have the same size with respect to the original object.
  • r:
    As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes.
  • t:
    Nearly correct, but argument has conceptual errors, or is incomplete.
  • 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.
  • y:
    Irrelevant discussion/effectively blank.
  • z:
Grading distribution:
Section 30882
Exam code: midterm01p0C4
p: 18 students
r: 2 students
t: 5 students
v: 11 students
x: 8 students
y: 0 students
z: 0 student

A sample "p" response (from student 1515):

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