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Kepler's Telescope Image Formation on the Retina, Assignments of Physics

University of Nebraska–Lincoln (UNL)Physics

Information about johannes kepler's discovery of the relationship between the length of the telescope's image on the retina and the distance between the observer and the telescope. It includes a recitation exercise problem that asks students to determine the length of the image on the retina when kepler was two meters closer to the telescope.

Typology: Assignments

Pre 2010

Uploaded on 08/30/2009

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Recitation Exercise #1, Physics 142, 8-22-00
Name
Example solution
___________
You can earn up to 15 points for the thoroughness of your explanation.
Johannes Kepler (1571-1630), a mathematician and astronomer, developed the first modern
theory of image formation on the eye's retina. One day, Kepler stood 10 meters away from
a telescope 1.5 meters long. As he stared at it, the images of the telescope on his retinas
were each 3.75-mm long. Absent-mindedly pondering the elliptical shape of planetary
orbits, he took a few steps toward the telescope and stopped when he was two meters
closer.
1. Is enough information given to determine the length of the telescope's images on
Kepler's retinas as he stood in his new position?
Yes, there is enough information to make a reasonable
approximation, if we ignore refraction in the eyeball and the
curvature of the retina.
2. If so, what was that length? If more information is needed, explain why, make
appropriate estimates, and work from them to estimate the length of the images.
Please support your response with appropriate diagram(s).
See the next page for an example solution.
pf2

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Recitation Exercise #1, Physics 142, 8-22-

Name Example solution ___________

You can earn up to 15 points for the thoroughness of your explanation.

Johannes Kepler (1571-1630), a mathematician and astronomer, developed the first modern theory of image formation on the eye's retina. One day, Kepler stood 10 meters away from a telescope 1.5 meters long. As he stared at it, the images of the telescope on his retinas were each 3.75-mm long. Absent-mindedly pondering the elliptical shape of planetary orbits, he took a few steps toward the telescope and stopped when he was two meters closer.

  1. Is enough information given to determine the length of the telescope's images on Kepler's retinas as he stood in his new position?

Yes, there is enough information to make a reasonable approximation, if we ignore refraction in the eyeball and the curvature of the retina.

  1. If so, what was that length? If more information is needed, explain why, make appropriate estimates, and work from them to estimate the length of the images.

Please support your response with appropriate diagram(s).

See the next page for an example solution.

In each diagram below, there is a pair of similar triangles; one between the two ends of the telescope and the pupil, and the other one between the ends of the retinal image and the pupil. Since the triangles are similar, we can write some ratios:

For the first picture (1.5 m) / (10 m) = (3.75 mm) / (eyeball length) For the second picture: (1.5 m) / (8 m) = (x mm) / (eyeball length)

Divide the top equation by the bottom equation, in order to avoid calculating the eyeball length: (8 m) / (10 m) = (3.75 mm) / (x mm) solve for x: x = (3.75 mm)*(10 m) / (8 m) x = 4.

The image is 4.7 mm long when the telescope is 8 m away. (This makes sense in terms of our experience that closer objects look larger!)

image on retina, 3.75 mm

Kepler's eyeball Kepler's telescope, 1.5 m

10 meters

pupil is a small light opening rays…

image on retina, x mm

Kepler's telescope, 1.5 m

8 meters