Physics midterm problem: extending telescope length

Physics 205B Midterm 1, spring semester 2017
Cuesta College, San Luis Obispo, CA

Two converging lenses, with focal lengths of +40.0 cm (for the objective lens) and +2.5 cm (for the eyepiece) are used to make a telescope. The length of the telescope (measured from lens-to-lens) is adjusted by sliding cardboard tubes in or out. Starting with the telescope used to look at an object very far away (essentially at infinity), determine how much the length must be extended in order to look at a closer object 10 m away. Show your work and explain your reasoning by using ray tracings and/or thin lens equations, properties of lenses, images, and magnification.


[*] Alan M. MacRobert, "Astronomy with a $5 Telescope," Sky & Telescope, vol. 79 no. 4 (April 1990), p. 384.

Solution and grading rubric:

• p:
  The eyepiece must be moved back by approximately 2 cm because:
  1. the object at d_o1 = +∞ for the objective creates a real image at d_i1 = f₁ = +40.0 cm, which becomes the object at a distance d_o2 = f₂ = +2.5 cm for the eyepiece, thus the telescope length (lens-to-lens distance) is 40.0 cm + 2.5 cm = 42.5 cm;
  2. the object at d_o1 = +10 m for the objective creates a real image at a slightly farther distance of d_i1 = +41.7 cm, which becomes the object at the same distance d_o2 = f2 = +2.5 cm for the eyepiece, thus the telescope length (lens-to-lens distance) is now slightly longer: 41.7 cm + 2.5 cm = 44.2 cm;
  3. thus the slight increase (approximately 2 cm) in the objective image distance d_i1 requires the eyepiece to be moved back by the same amount in order for this image to be placed at its front focal point.
• 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 approach has conceptual errors, and/or major/compounded math errors. At least understands that the telescope length is f₁ + f₂ when focused at ∞, and some attempt at finding the telescope length d_i1 + f₂ when focused at a finite d_o1.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some garbled attempt at ray tracings and/or thin lens equations, the properties of lenses, images, and magnifications. May have used microscope magnification equation to find length between lenses.
• x:
  Implementation/application 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: midterm01AhC4
p: 5 students
r: 0 students
t: 7 students
v: 17 students
x: 1 student
y: 0 students
z: 0 students

A sample "p" response (from student 1412):