Physics final exam problem: IMAX projector lens focal length

Physics 205B Final Exam, spring semester 2012
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Review and Synthesis Problem 7, p. 963

The projector at the British Film Institute IMAX movie theater in London, UK[*] projects an image of 70.0 mm wide film onto a 26.0 m wide screen that is located at a distance of 25.8 m from the projector lens. Solve for the focal length of the projector lens, assuming that it can be approximated by a thin converging lens. Show your work and explain your reasoning.

[*] bfi.org.uk/about/venuehire/pdf/imax_technical_guide.pdf.

Solution and grading rubric:

• p:
  Correct. From an object height of +0.070 m, image height of –26 m (as it is inverted with respect to the object), and image distance of +25.8 m, finds the object distance; then uses thin lens equation to find focal length f.
  
• r:
  Nearly correct, but includes minor math errors. Typically has negative sign error in the object height (resulting in negative object distance), which is either carried through to find (slightly erroneous) f, or assumes positive object distance to find f.
  
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least has object distance.
  
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner.
  
• x:
  Implementation of ideas, but credit given for effort rather than merit.
  
• y:
  Irrelevant discussion/effectively blank.
  
• z:
  Blank.
  

Grading distribution:
Section 30882
Exam code: finalsM0k
p: 5 students
r: 11 students
t: 4 students
v: 4 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 0801), explicitly solving for the object distance before solving for the focal length f:
Another sample "p" response (from student 1992), algebraically eliminating the object distance in solving for the focal length f (with rounding errors to find the numerical result):