20160327

Physics midterm question: comparing converging lens image sizes

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

An object is placed 20 cm in front of a f = +5.0 cm converging lens, which produces an image. When the object then placed 10 cm in front of this lens, discuss why this image is not twice as large as the previous image. Explain your reasoning by using ray tracings and/or thin lens equations, the properties of lenses, images, and magnification.

Solution and grading rubric:
• p:
Correct. Discusses/demonstrates that the image (or linear magnification) produced by the object 10 cm in front of the lens is not twice the image (or linear magnification) produced the same object placed 20 in front of the lens from:
1. calculating the image distances produced by the different object distances, and finds the resulting respective image sizes 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.
• 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 properties of lenses, images, and linear magnification.
• 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: midterm01rx1C
p: 35 students
r: 3 students
t: 4 students
v: 1 student
x: 0 students
y: 0 students
z: 0 student

A sample "p" response (from student 9490), solving the thin lens equations:

Another sample "p" response (from student 1337), using ray tracings:

Another sample "p" response (from student 5504), using both thin lens equations and ray tracings: