Physics midterm question: increasing DVD (grating) to screen distance

Physics 205B Midterm 1, spring semester 2016
Cuesta College, San Luis Obispo, CA

A red laser (wavelength 632 nm) illuminates a transparent DVD (digital videodisc) with a track spacing[*] of 740 nm, producing a central and two first maxima spots on a screen (drawing at right is not to scale). While the positions of the laser and the screen are kept constant, the DVD is moved slightly to the left, closer to the laser (and farther from the screen). Discuss why the spacing of the maxima spots as measured along the screen will change as a result. 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. Proves that the spacing of the maxima spots on the screen would increase because:
  1. the spacing d between tracks, the wavelength λ of the laser would not be affected, such that the θ angle of the first maxima would also not be affected, and;
  2. from trigonometry (or properties of similar right triangles), as the θ angle of the first maxima remains constant, as the horizontal (adjacent) right triangle leg increases, the vertical (opposite) leg must increase.
• 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. 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.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 30882, 30883
Exam code: midterm01rx1C
p: 21 students
r: 0 students
t: 11 students
v: 7 students
x: 4 students
y: 0 students
z: 0 students

A sample "p" response (from student 7399):