Physics midterm question: implausible Instagram filter

Physics 205B Midterm 1, spring semester 2014
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 23.65

Two photos[*][**] of the same sunset are shown above, where the second image apparently has a fishbowl effect added to it. Assuming that this fishbowl is a spherical glass bowl filled with water, discuss why this second image cannot be a plausible realistic effect. Explain your reasoning using the properties of lenses, thin lens equations and/or ray tracings.

[*] weheartit.com/entry/91939793/via/_Lientje.
[**] instagram.com/p/kuXP8jq0a9/.

Solution and grading rubric:
  • p:
    Correct. Understands that (a) a spherical fishbowl filled with water would behave as a converging lens, and uses a ray diagram, thin lens equation(s), and/or properties of lenses in general to discuss contradictions due to either (i) sun and horizon well outside of the focal point of converging lens should produce a diminished, inverted image (which is instead upright and appears to be the same size), or (ii) upright image must be virtual, which can only be caused by object well inside of the focal length of a converging lens (not plausible for the sun/horizon), or an object near a diverging lens (which would not be a spherical water-filled fishbowl).
  • 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:
Sections 30882, 30883
Exam code: midterm01b0w7
p: 15 students
r: 8 students
t: 13 students
v: 3 students
x: 2 students
y: 0 students
z: 0 students

A sample "p" response (from student 1216):

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