20150624

Physics final exam question: converging lens image same size as object

Physics 205B Final Exam, spring semester 2015
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 23.63

A Physics 205B student places a object 22 cm in front of (to the left of) a converging lens (f = +11 cm). Discuss why the size of resulting image will be exactly the same size as the original object. Explain your reasoning by using the properties of lenses, thin lens equations and/or ray tracings.

Solution and grading rubric:
  • p:
    Correct. Image will be the same size as the original object because:
    1. from the thin lens equation, the image distance di will be the same as the object image distance do;
    2. and from the linear magnification equation, the image height h' will be –hdi/do, which makes the image the same size as (but inverted from) the original object.
  • r:
    As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. Typically shows that do = di, but does not explicitly relate this to how the image and object sizes compare.
  • 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:
    Blank.
Grading distribution:
Sections 30882, 30883
Exam code: finalLd0c
p: 16 students
r: 18 students
t: 2 students
v: 2 students
x: 1 student
y: 1 student
z: 3 student

A sample "p" response (from student 5425):

A sample "r" response (from student 1675):

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