Physics midterm question: comparing diverging lens image sizes

Physics 205B Midterm 1, spring semester 2019
Cuesta College, San Luis Obispo, CA

An object 1.0 cm in height is placed 16.0 cm in front of a f = –15.0 cm diverging lens, producing an image. Show that moving the object slightly closer, such that it is 14.0 cm in front of this diverging lens will result in a slightly larger image than before. Explain your reasoning by using ray tracings and/or thin lens equations, properties of lenses, images, and magnification.

Solution and grading rubric:

• p:
  Correct. Proves that the object should be as close to the diverging lens as possible in order to obtain the largest image (largest linear magnification factor) using either of these two methods:
  1. calculating the image distances produced by the different object distances, and finds the resulting respective image sizes and/or linear magnification factors; or
  2. drawing two carefully, properly scaled ray tracing diagrams.
• 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 misplaced values, but consistently interprets resulting numbers.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. Problematic algebra (combines fractions by combining denominators, forgets to invert (1/f – 1/d_o) to solve for d_i, etc.).
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some garbled attempt at applying properties of lenses, images, and linear magnification. Typically has problematic algebra as in (t), but does not use (erroneous) d_i values to find image heights or linear magnification factors for comparison.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. No clear attempt at applying properties of lenses, images, and angular magnification.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 30882, 30883
Exam code: midterm01Ft6G
p: 25 students
r: 6 students
t: 4 students
v: 4 students
x: 2 students
y: 0 students
z: 0 students

A sample "p" response (from student 1810), using two sets of thin lens equations:
Another sample "p" response (from student 0691), using two ray tracings: