Physics final exam question: optical fiber core vs. cladding

Physics 205B Final Exam, spring semester 2014
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 23.25, Comprehensive Problem 23.93

An undergraduate physics project describes the total internal reflection that occurs in the core and cladding of optical fibers:
Light is trapped in an inner transparent solid core wrapped with a second material (cladding) of higher index of refraction[*].
Discuss why this statement comparing the core and cladding indices of refraction is incorrect. Explain your reasoning using the properties of light and refraction.

[*]D. D. Diba, "Optical Photonic Bandgap Fibers," May 11, 2010, Department of Physics, Umeå University, Sweden, tp.umu.se/advmat/FinalProjects/Photonic%20Bandgap%20Fibers.pdf.

Solution and grading rubric:
  • p:
    Correct. If the incident ray (in the core) is in the lower refraction index material than the higher refraction index cladding, then there cannot be total internal reflection, as the critical angle (which the incident angle would need to be less than) would be undefined. Demonstrates this using Snell's law and/or the critical angle equation.
  • 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. Recognizes that total internal reflection cannot occur with a lower refraction index core and higher refraction index cladding, but does not substantiate this claim.
  • v:
    Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some attempt at using Snell's law, critical angle, and or total internal reflection concepts.
  • 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: finalEL7a
p: 9 students
r: 7 students
t: 5 students
v: 7 students
x: 2 student
y: 2 students
z: 0 students

A sample "p" response (from student 6893):

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