Physics midterm problem: diverging lens and converging lens

Physics 205B Midterm 1, spring semester 2018
Cuesta College, San Luis Obispo, CA

An object 1.0 cm in height is placed 5.0 cm in front of a f = –20.0 cm diverging lens, producing an upright image. This same 1.0 cm high object is then placed an unknown distance in front of a f = +20.0 cm converging lens, producing an inverted image that is the same size as the upright image originally produced by the diverging lens.

Determine (a) the size of the image produced by the diverging lens, and (b) the distance of this object in front of the f = +20.0 cm converging lens.

Show your work and explain your reasoning by using ray tracings and/or thin lens equations, properties of lenses, images, and magnification.

Solution and grading rubric:

• p:
  Correct. Identifies relevant parameters to methodically use the thin lens equation and linear magnification equation, in order to determine:
  1. that for the diverging lens, h_o = +1.0 cm, d_o = +5.0 cm, f = −20.0 cm, and uses thin lens equation to either find d_i = −4 cm (a virtual image) to find image height h_i = +0.8 cm (upright image) from the linear magnification equation, or may eliminate d_i in both equations to solve for h_i directly; and
  2. for the converging lens, h_o = +1.0 cm (the same object), d_o and d_i are both unknown, f = +20.0 cm, and h_i = −0.8 cm (inverted image that is the same size as the upright image produced by the diverging lens), and eliminates d_i in both equations to find d_o = +45 cm. May include very minor math errors with handling fractions and inverses.
• r:
  Nearly correct, but includes minor math conceptual errors, typically overlooking the fact that the image produced by the converging lens is inverted.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least solves for (1) successfully, and still attempts to methodically use this information in (2) to solve for the object distance for the converging lens. Typically makes multiple conceptual errors, such as overlooking the fact that the image produced by the converging lens is inverted; claiming that the image distance for the converging lens is the same as the image distance for the diverging lens, etc.
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Some garbled attempt at ray tracings and/or thin lens equations, the properties of lenses, images, and magnifications.
• x:
  Implementation of ideas, but credit given for effort rather than merit. No clear attempt at applying ray tracings and/or thin lens equations, the properties of lenses, images, and magnifications.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 30882, 30883
Exam code: midterm01cVdP
p: 4 students
r: 7 students
t: 24 students
v: 0 students
x: 0 students
y: 0 students
z: 0 student

A sample "p" response (from student 7164):