Cuesta College, San Luis Obispo, CA
Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 24.1
[20 points.] An upright object is placed 10.0 cm to the left of a diverging lens with focal length –15.0 cm. A second converging lens with focal length +8.0 cm is to be placed to the right of the first lens. What is the minimum separation distance (in cm) between the first lens and second lens such that the second lens will be able to produce a real final image? Show your work and explain your reasoning.
Solution and grading rubric:
- p = 20/20:
Correct. Determines that the first diverging lens will produce a virtual image located 6.0 cm in front of it. For the second converging lens to produce a real image, its object must be located outside of its secondary focal point, which is 8.0 cm in front of it. Since the image from the first lens will be the object for the second lens, the second lens must be placed at a minimum distance of 2.0 cm behind the first lens in order for the second lens to produce a final real image.
- r = 16/20:
Nearly correct, but includes minor math errors. May have not sufficiently explained the conditions for the second lens to create a real image in terms of its object and focal length positions.
- t = 12/20:
Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least determined the location of the image produced by the first lens, and some attempt at constraining the location of the second lens.
- v = 8/20:
Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner.
- x = 4/20:
Implementation of ideas, but credit given for effort rather than merit.
- y = 2/20:
Irrelevant discussion/effectively blank.
- z = 0/20:
p: 7 students
r: 1 student
t: 3 students
v: 3 students
x: 0 students
y: 0 students
z: 0 students
A sample "p" response (from student 7673):
Another sample "p" response (from student 0097):