Physics midterm question: microscope object distance and barrel length

Physics 205B Midterm 1, spring semester 2015
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 24.37

A microscope has a "barrel length" (distance from lens-to-lens) of 20 cm when an object is placed at a certain distance in front of the objective lens. Discuss why the barrel length of the microscope must increase if the object distance in front of the object lens is decreased. Explain your reasoning by using a ray tracing and/or thin lens equations, the properties of lenses, images, and magnification.

Solution and grading rubric:

• p:
  Correct. Discusses/demonstrates:
  1. the objective takes an object in front of it (outside of its focal point), and makes a real image behind it;
  2. the location of the real image produced by the objective determines the placement of the focal point of the eyepiece, which sets the barrel length of the microscope (between the inside focal lengths);
  3. thus from the thin lens equation decreasing the object distance (while d_o1 is still greater than f) will increase d_i1, which then must increase the barrel length of the microscope.
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. Typically discusses (1) and (3), but does not explicitly show (2) how the placement of the eyepiece must be moved back, which increases the barrel length.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. Has only one of the three points in (p).
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some garbled attempt at applying applying properties of lenses, images, and angular magnification.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. Approach other than that of applying properties of lenses, images, and angular magnification.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 30882, 30883
Exam code: midterm01p34K
p: 17 students
r: 4 students
t: 4 students
v: 11 students
x: 1 student
y: 0 students
z: 0 student

A sample "p" response (from student 8518):