The Physics
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Opus in profectus

The Nature of Light

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Practice

practice problem 1

Use Rømer's method and Rømer's numbers to determine the speed of light in a vacuum. If you're comfortable reading Seventeenth Century French, here's the paragraph that reports Rømer's measurement of a 22 minute delay as the light from Jupiter's moon Io traverses the extra distance equal to the diameter of earth's orbit (represented by HE on a diagram in the report).

Il ne s'ensuit pas pourtant que la lumière ne demande aucun temps : car après avoir examiné la chose de près, il a trouvé que ce qui n’était pas sensible en deux révolutions devenait très considérable à l'égard de plusieurs prises ensemble, et que par exemple quarante révolutions, observées du côté F, étaient sensiblement plus courtes que quarante autres, observées de l'autre côté en quelque endroit du zodiaque que Jupiter se soit rencontré ; et ce à raison de 22 pour tout l’intervalle HE, qui est le double de celui qu’il y a d'ici au soleil

Ole Rømer, 1676

I couldn't find any astronomical measurements from Rømer's day, so here are the currently accepted values.

quantity earth jupiter
distance to sun (106 km) 149.6 778.6
orbital period (days) 365.25 4331
length of day (hours) 24.0 9.9
  1. Sketch the sun, Earth, and Jupiter when…
    1. the earth is closest to Jupiter
    2. the earth is farthest from Jupiter
  2. Determine the speed of light in a vacuum using Rømer's method.

solution

Answer it.

practice problem 2

A common measure of astronomical distances is the light year. This is the distance a beam of light would travel in a vacuum in one year. Determine the size of a light year in meters using the speed of light.

solution

Answer it.

practice problem 3

The Speed of Dark
What if one fine evening, as the sun was setting and a full moon was rising, the sun suddenly quit emitting light?
  1. How soon after the sun went black would we know about it on earth?
  2. Sketch the relative positions of the sun, earth, and moon at the time described above.
  3. How soon before or after we saw the sun go dark would the moon cease shining?
  4. What is the speed of dark?

solution

  • Answer it! What is the speed of dark?

practice problem 4

Write something completely different.

solution

Answer it.