Physics midterm question: comparing first and second maxima angles

Physics 205B Midterm 1, spring semester 2017
Cuesta College, San Luis Obispo, CA

A green laser (wavelength 550 nm) illuminates a compact disc (CD) disk with a track spacing of 1.6 µm[*], producing a set of maxima spots at certain angles. (Drawing is not to scale.) Discuss why the second maxima angle is not exactly twice the first maxima angle. Explain your reasoning using trigonometry, the properties of source phases, path lengths, and interference.

[*] en.wikipedia.org/wiki/File:Comparison_CD_DVD_HDDVD_BD.svg

Solution and grading rubric:

• p:
  Correct. The second maxima angle is not exactly twice the first maxima angle, because given spacing d between tracks and the wavelength λ of the laser, from the maxima equation d·sinθ = m·λ the first maxima angle θ₁ = sin^–1(1·λ/d), and the second maxima angle θ₂ = sin^–1(2·λ/d), which is slightly more than twice θ₁.
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. May have solved for second minima angle instead of second maxima angle.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. At least has first maxima angle, or sets up work that would eventually result in finding and comparing first maxima angle with the second maxima angle.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some garbled attempt at applying trigonometry, properties of source phases, path lengths, and interference.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. No clear attempt at applying trigonometry, properties of source phases, path lengths, and interference. Focus on constructing triangles with CD-to-screen distance and spacing along screen distance to find angles, rather than appealing to properties of constructive interference along certain angles.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 30882, 30883
Exam code: midterm01AhC4
p: 17 students
r: 2 students
t: 5 students
v: 1 student
x: 5 students
y: 0 students
z: 0 students

A sample "p" response (from student 2420):