Overview

Lesson Procedure

60-65 minutes of class time across 5 phases.

1. Warm-Up5 minutes
2. Direct Instruction15-20 minutes
3. Guided Practice15 minutes
4. Independent Practice20 minutes
5. Closure5 minutes

1. Warm-Up5 minutes

   Project three statements about one question, "How long does the school's late bus take to get home?": a bus company brochure ("about 20 minutes"), a student's phone timer log for five rides (24, 31, 22, 27 and 26 minutes), and a parent's short video of the bus stuck behind a train.

   Warm-Up Prompt

   Using all three sources, what would you tell a new student, and which source did you trust most for the number? Write two sentences.

   Take answers. Strong ones use the log for the number (a mean of 26 minutes, from 22 to 31), use the video to explain the slow days, and treat the brochure's 20 minutes as a best case the log does not support. Tell students that this is today's skill. RST.11-12.7 asks them to integrate and evaluate multiple sources of information presented in diverse formats and media, such as quantitative data, video and multimedia, in order to address a question or solve a problem. Integrating means combining the sources into one answer; evaluating means judging what each source is good for and where it is wrong.

2. Direct Instruction15-20 minutes

   Part 1: The question and the sources. Today's question is How fast does light travel, and how far can we trust the answer Albert Michelson published in 1880? Michelson, then a young instructor at the U.S. Naval Academy in Annapolis, timed light over a baseline of about 2,000 feet with a rapidly turning mirror. Students will integrate seven sources in four formats: Michelson's own text (Sources 1 and 3), his data tables (Source 2: Diagram 1 and the table below), an online video (Source 4), a table of modern reference values (Source 5), and, in the homework, a 1900 astronomy book and a modern fact card (Sources 6 and 7). Post the four moves:

   1. State the question, and what each source can contribute to it.
   2. Put the numbers on one scale: same units, same conditions (in air or in a vacuum, before or after corrections).
   3. Check each claim against the source best placed to settle it.
   4. Weigh the sources: say which you trust for which part of the answer, and why.

   1These experiments, made with very crude apparatus and under great difficulties, gave the following table of results for the velocity of light in miles per second:

   2186730
   188820
   186330
   185330
   187900
   184500
   186770
   185000
   185800
   187940
   ------
   Mean 186500 ± 300 miles per second,
   or 300140 kilometers per second.

   3In the following July the sum of $2,000 was placed at my disposal by a private gentleman for carrying out these experiments on a large scale. Before ordering any of the instruments, however, it was necessary to find whether or not it was practicable to use a large distance. With a distance (between the revolving and the fixed mirror) of 500 feet, in the preliminary experiments, the field of light in the eye-piece was somewhat limited, and there was considerable indistinctness in the image, due to atmospheric disturbances.

   4Accordingly, the same lens (39 feet focus) was employed, being placed, together with the other pieces of apparatus, along the north sea-wall of the Academy grounds, the distance being about 2,000 feet. The image of the slit, at noon, was so confused as not to be recognizable, but toward sunset it became clear and steady, and measurements were made of its position, which agreed within one one-hundredth of a millimeter. It was thus demonstrated that with this distance and a deflection of 100 millimeters this measurement could be made within the ten-thousandth part.

   5In order to obtain this deflection, it was sufficient to make the mirror revolve 250 times per second and to use a "radius" of about 30 feet. In order to use this large radius (distance from slit to revolving mirror), it was necessary that the mirror should be large and optically true; also, that the lens should be large and of great focal length. Accordingly the mirror was made 1¼ inches in diameter, and a new lens, 8 inches in diameter, with a focal length of 150 feet was procured.

   [...]

   6The first observation with the new lens was made January 30, 1879. The deflection was 70 millimeters. The image was sufficiently bright to be observed without the slightest effort. The first observation with the new micrometer eye-piece was made April 2, the deflection being 115 millimeters.

   7The first of the final series of observations was made on June 5. All the observations previous to this, thirty sets in all, were rejected. After this time, no set of observations nor any single observation was omitted.

   Source 2, part B: Michelson's table of results for groups of observations, velocity of light in air in km/s, as printed in 1880 (number of sets in parentheses). Part A is Diagram 1, drawn from his table of all 100 readings.

   Group of observations	Result
   Electric light (1 set)	299850
   Set micrometer counting oscillations (2)	299840
   Readings taken by Lieutenant Nazro (3)	299830
   Readings taken by Mr. Clason (5)	299860
   Mirror inverted (8)	299840
   Speed of rotation, 192 (7)	299990
   Speed of rotation, 128 (1)	299800
   Speed of rotation, 96 (1)	299810
   Speed of rotation, 64 (1)	299870
   Radius, 28.5 feet (54)	299870
   Radius, 33.3 feet (46)	299830
   Highest temperature, 90° Fahr. (5)	299910
   Mean of lowest temperatures, 60° Fahr. (7)	299800
   Image, good (46)	299860
   Image, fair (39)	299860
   Image, poor (15)	299810
   Frame, inclined (5)	299960
   Greatest value	300070
   Least value	299650
   Mean value	299852
   Average difference from mean	60
   Value found for π	3.26
   Probable error	± 5

   Source 5: Modern reference values used in this lesson

   Quantity	Value
   Speed of light in a vacuum (exact, since the definition of the meter adopted in 1983)	299,792.458 km/s, about 186,282 miles per second
   One mile	1.609344 km (exact)
   One foot	0.3048 m (exact)
   Index of refraction of air near sea level and room temperature	about 1.0003, so light in air is about 90 km/s slower than in a vacuum

   • Integrating a text with the data inside it (Source 1, paragraphs 1-2)

     Michelson prints ten results from 1878 and says they came from "very crude apparatus." Check his mean and his conversion, and say what the ten numbers add to his words.

     Result: The ten values add to 1,865,120, so the mean is 186,512 miles per second, which he rounds to 186,500. Converting with Source 5: 186,500 × 1.609344 ≈ 300,143 km/s, matching his 300,140. The numbers show what "crude" means: single trials run from 184,500 to 188,820, a spread of 4,320 miles per second, more than 2 percent of the mean. The words tell a reader the method was rough; the data tell how rough, and paragraphs 3-5 then explain the changes (a longer baseline of about 2,000 feet and a larger deflection) that were meant to fix it.

   • Putting three sources on one scale (Diagram 1, Source 3, Source 5)

     Diagram 1 shows the 100 readings as Michelson recorded them. Where does today's speed of light belong on that scale, and what does its position tell you about the kind of error in the 1879 result?

     Result: The readings are speeds in air before corrections. Source 3 adds +12 km/s for temperature and +80 km/s to go from air to a vacuum, 92 km/s in all. To compare like with like, subtract the same 92 from today's vacuum value: 299,792.458 - 92 ≈ 299,700 km/s. Only 2 of the 100 readings (299,620 and 299,650) lie below that line. If the method had only random error, the readings would scatter on both sides of the true value; instead almost the whole set sits high. That is a systematic error, and averaging more readings could not have removed it. No single source shows this: it takes the data, Michelson's corrections and the modern value together.

   Close the model: the integrated answer is not a list of what each source says. It is one claim ("Michelson's readings were precise but sat about 150 km/s high") that no single source makes, supported by all three.

3. Guided Practice15 minutes

   Pairs read the video transcript (Source 4), written for this page, and mark each statement C (can be checked in Sources 1-3 and 5), O (needs an outside source) or F (framing or opinion). Then work the two examples as a class.

   1[Transcript of the segment "Racing a Beam of Light," episode 2 of an online science series, 4 minutes 10 seconds long. The series, its narrator and its graphics are invented for teaching. What appears on screen is described in brackets.]

   2[On screen: a mirror spinning in slow motion.] NARRATOR: In the summer of 1879, a 26-year-old Navy instructor named Albert Michelson set out to time the fastest thing in the universe. His trick was a small mirror spinning about 257 times every second.

   3[On screen: an animated map of the Naval Academy sea wall, with a line labeled "Light's round trip: 3,972 feet."] NARRATOR: A beam of light bounced off the spinning mirror, raced to a fixed mirror far down the sea wall and came back. The round trip took about four millionths of a second. In that time the spinning mirror turned only about a thousandth of a turn, so the returning beam came back a little off course, shifted by about 11 to 13 centimeters. Measure that shift, and you can work out the speed of light.

   4[On screen: a stack of handwritten pages.] NARRATOR: Michelson repeated the measurement a hundred times, and he never threw away a single result.

   5[On screen: a bar chart titled "Michelson Nailed It." Two bars are labeled "Michelson, 1879: 299,944 km/s" and "Today: 299,792 km/s." The vertical axis runs from 299,700 to 300,000.] NARRATOR: His answer, 186,380 miles per second, matches today's value almost exactly, and it was well inside his own margin of error. Other scientists soon agreed: the French physicist Alfred Cornu had found 300,400 kilometers per second with a spinning toothed wheel.

   6[On screen: the words "c = 299,792.458 km/s. Exactly."] NARRATOR: Today the speed of light is fixed by definition at exactly 299,792.458 kilometers per second, so there is nothing left to measure.

   • Checking a video's numbers against the primary source (Source 4, paragraph 3)

     The video says the round trip was 3,972 feet and "took about four millionths of a second," and that the mirror "turned only about a thousandth of a turn." Do Michelson's figures support all three?

     Result: Source 1, paragraph 4, gives a distance of "about 2,000 feet," so a round trip of about 4,000 feet fits the video's 3,972. In meters, 3,972 × 0.3048 ≈ 1,211 m, and at about 299,900 km/s the trip takes 1,211 ÷ 299,900,000 ≈ 0.00000404 s, about 4.0 millionths of a second. Source 3, paragraph 7, puts the usual speed at 256 turns per second, and 256 × 0.00000404 ≈ 0.0010 of a turn. All three claims check out, and they agree with each other.

   • Sorting statements by how they can be checked (Source 4, paragraph 2)

     Evaluate three statements: Michelson was "a 26-year-old Navy instructor," the mirror spun "about 257 times every second," and he set out "to time the fastest thing in the universe."

     Result: The age needs an outside source: none of these texts gives it. A biography gives his birth in December 1852, so he was 26 in the summer of 1879 and the claim is right, but a student must name that source. The spin rate can be checked: Source 3, paragraph 7, says the speed "was lowered from 256 turns," so 257 is a slightly different rounding of the same figure. "The fastest thing in the universe" is framing: true as physics, but it is not evidence about the experiment. A video mixes these kinds of statement, so each needs its own test.

   Debrief: Which of the video's statements could you not check yet? Students usually list the claims about "a hundred times," the bar chart, the margin of error and Cornu. Those need Michelson's own final section, which students read next.

4. Independent Practice20 minutes

   Students read Source 3, from the end of Michelson's paper, on their own and answer quiz questions 1-20, using all the sources on this page. Before they read, explain three terms: "in vacuo" means in a vacuum; Michelson's "±51 kilometers" is his limit on the error, in the most unfavorable case; and Alfred Cornu was a French physicist who had timed light with a rapidly turning toothed wheel a few years earlier. Friedrich Helmert, a German geodesist, later recalculated Cornu's result.

   1Summing up the various errors, we find, then, that the total constant error, in the most unfavorable case, where the errors are all in the same direction, would be .00015. Adding to this the probable error of the result, .00002, we have for the limiting value of the error of the final result ±.00017. This corresponds to an error of ±51 kilometers.

   2The correction for the velocity of light in vacuo is found by multiplying the speed in air by the index of refraction of air, at the temperature of the experiments. The error due to neglecting the barometric height is exceedingly small. This correction, in kilometers, is +80.

   3Final Result.

   4The mean value of V from the tables is 299852
   Correction for temperature +12
   ------------
   Velocity of light in air 299864
   Correction for vacuo 80
   ------------
   Velocity of light in vacuo 299944±51

   5The final value of the velocity of light from these experiments is then--299940 kilometers per second, or 186380 miles per second.

   [...]

   6Change of Speed of Rotation.

   7In the last four sets of observations the speed was lowered from 256 turns to 192, 128, 96, and 64 turns per second. The results with these speeds were the same as with the greater speed within the limits of errors of experiment.

   8Bias.

   9Finally, to test the question if there were any bias in taking these observations, eight sets of observations were taken, in which the readings were made by another, the results being written down without divulging them. Five of these sets are given in the "specimen," pages 133-134.

   10It remains to notice the remarkable coincidence of the result of these experiments with that obtained by Cornu by the method of the "toothed wheel."

   11Cornu's result was 300400 kilometers, or as interpreted by Helmert 299990 kilometers. That of these experiments is 299940 kilometers.

5. Closure5 minutes

   Exit ticket: "Answer today's question in three sentences. Use at least one number from Michelson's data, one from Source 5 and one judgment about the video, and name the source of each." Sort the tickets into "integrated," "listed source by source" and "one source only."

   Teacher note on the historical texts. Michelson's paper is printed as published in 1880; its "±51 kilometers" is a limit he computed from the known sources of error, not a statistical range in the modern sense. Two figures in his table of groups (Source 2, part B) do not match his table of all 100 readings: the least value there is 299,650, but the full table includes 299,620 (June 18), and the seven sets at about 192 turns per second average about 299,909 in the full table, not 299,990. Both are printed here as in the source; quiz question 7 uses the first. Michelson went on to make better measurements of the speed of light over the next fifty years, and in 1907 he received the Nobel Prize in Physics for his optical instruments and the measurements made with them. The texts have no dated or offensive language.

   Homework sources. The homework uses a passage from Robert S. Ball's astronomy book The Story of the Heavens (Source 6) and a modern fact card written for this page (Source 7). Ball writes "Roemer" for the Danish astronomer Ole Rømer; Rømer's result is usually dated 1676, the year he announced it, not Ball's 1675.

   1[...] It was noticed that when the earth was near to Jupiter the eclipse generally occurred before the predicted time; while when the earth happened to be at the side of its orbit away from Jupiter, the eclipse occurred after the predicted time. Once this was proved, the great discovery was quickly made by Roemer, a Danish astronomer, in 1675. [...] We learned from it that light had a measurable velocity, which, according to recent researches, amounts to 186,300 miles per second.

   [...]

   2It thus appears that we can tell the velocity of light either by the observations of Jupiter's satellites or by experimental enquiry. If we take the latter method, then we are entitled to deduce remarkable astronomical consequences. We can, in fact, employ this method for solving that great problem so often referred to--the distance from the earth to the sun--though it cannot compete in accuracy with some of the other methods.

   3The dimensions of the solar system are so considerable that a sunbeam requires an appreciable interval of time to span the abyss which separates the earth from the sun. Eight minutes is approximately the duration of the journey, so that at any moment we see the sun as it appeared eight minutes earlier to an observer in its immediate neighbourhood. In fact, if the sun were to be suddenly blotted out it would still be seen shining brilliantly for eight minutes after it had really disappeared. We can determine this period from the eclipses of Jupiter's satellites.

   4So long as the satellite is shining it radiates a stream of light across the vast space between Jupiter and the earth. When the eclipse has commenced, the little orb is no longer luminous, but there is, nevertheless, a long stream of light on its way, and until all this has poured into our telescopes we still see the satellite shining as before. If we could calculate the moment when the eclipse really took place, and if we could observe the moment at which the eclipse is seen, the difference between the two gives the time which the light occupies on the journey. This can be found with some accuracy; and, as we already know the velocity of light, we can ascertain the distance of Jupiter from the earth; and hence deduce the scale of the solar system. It must, however, be remarked that at both extremities of the process there are characteristic sources of uncertainty. The occurrence of the eclipse is not an instantaneous phenomenon. The satellite is large enough to require an appreciable time in crossing the boundary which defines the shadow, so that the observation of an eclipse cannot be sufficiently precise to form the basis of an important and accurate measurement. [...]

   1The average distance. The average distance from Earth to the Sun is called the astronomical unit (au). Since 2012, astronomers have fixed it at exactly 149,597,870.7 km, about 92.96 million miles. Light crosses it in about 499.0 seconds, or 8 minutes 19 seconds.

   2Not a perfect circle. Earth's orbit is slightly oval. Early each January, Earth is closest to the Sun, about 147.1 million km away; early each July it is farthest, about 152.1 million km away. The seasons come from the tilt of Earth's axis, not from this change in distance.

   3How we know. Modern distances in the solar system come from timing signals. Radar pulses bounced off the planets since the early 1960s, and radio signals sent to spacecraft, travel at the speed of light, so a distance is half the round-trip time of a signal multiplied by the speed of light. Before radar, astronomers found the distance of the Sun from careful angle measurements of Venus and Mars, and from the speed of light combined with its travel time.

Differentiation Strategies

Assessment Guidance

1. Question 1 of 20 · Multiple Choice

   Which statement correctly fits Diagram 1 together with Source 3?

   AIts balance point, near 299,852, is the tables' mean; the final value adds 92 km/s BThe histogram already includes both corrections, so its center is the final value of 299,944 CThe tallest bar of the histogram marks the final value Michelson reports in paragraph 4 DThe final value in paragraph 4 is the midpoint of the highest and lowest readings

2. Question 2 of 20 · Multiple Choice

   The video says Michelson "never threw away a single result" (Source 4, paragraph 4). Which evaluation is best supported by Michelson's own text?

   AThe claim is true: Source 3 says the results with every speed of rotation agreed BTrue only of the final series: Source 1 says thirty earlier sets were rejected CThe claim is false: Diagram 1 shows that the readings below 299,650 were dropped DThe claim cannot be checked, because Michelson never says what he did with his results

3. Question 3 of 20 · Multiple Choice

   The video's bar chart (Source 4, paragraph 5) starts its axis at 299,700. Which evaluation of the chart is accurate?

   AIt is accurate, because both bars show the correct values from Michelson and from Source 5 BIt is misleading, because Michelson's value should be shown in miles per second, not in km/s CMisleading: from a base of 299,700, a gap of about 150 km/s looks over 2.5 times as tall DIt is misleading, because the modern value should appear as the taller of the two bars

4. Question 4 of 20 · Multiple Choice

   By what percent does Michelson's final 299,944 km/s (Source 3) differ from the modern value in Source 5?

   AAbout 0.5 percent BAbout 5 percent CAbout 0.03 percent DAbout 0.05 percent

5. Question 5 of 20 · Multiple Choice

   The video says Michelson's answer "was well inside his own margin of error" (Source 4, paragraph 5). Which evaluation is correct?

   AFalse: he is about 150 km/s above today's value, three times his limit of 51 BTrue: his value is about 150 km/s above today's, well under his stated limit of 510 CTrue: today's value lies between his lowest and highest single readings in Diagram 1 DFalse: his stated limit was 51 percent, far too large to be a useful margin

6. Question 6 of 20 · Multiple Choice

   Which group in Source 2, part B, together with which paragraph of Source 3, best tests whether Michelson's expectations could have influenced his readings?

   A"Radius, 28.5 feet" and "Radius, 33.3 feet," with paragraph 7 on the speed of rotation BThe readings taken by Lieutenant Nazro and by Mr. Clason, with paragraph 9 on bias C"Image, good," "Image, fair" and "Image, poor," with paragraph 1 on the constant error D"Highest temperature" and "lowest temperatures," with paragraph 2 on the vacuum correction

7. Question 7 of 20 · Multiple Choice

   Source 2, part B, lists the "Least value" as 299,650, but Diagram 1 shows one reading in the bin from 299,600 to 299,649. What is the best conclusion?

   ADiagram 1 must be wrong, because a summary table is always more reliable than the data BThe low reading was a correction added after the summary table was printed CThe two parts of Source 2 disagree, so one of Michelson's summaries has an error DThe difference is too small to matter, so a careful reader should ignore it

8. Question 8 of 20 · Multiple Choice

   Michelson calls his agreement with Cornu a "remarkable coincidence" (Source 3, paragraph 10). Which evaluation fits paragraph 11?

   AIt is fully supported: Cornu's own result, 300,400, is within 51 km/s of Michelson's BIt is not supported at all: both of Cornu's figures are more than 400 km/s away CIt is supported only by Cornu's own figure; Helmert's recalculation disagrees with it DIt is supported only by Helmert's 299,990; Cornu's own is 460 km/s higher

9. Question 9 of 20 · Multiple Choice

   Single 1878 trials in Source 1, paragraph 2, run from 184,500 to 188,820 miles per second. Using the greatest and least values in Source 2, part B, for the 1879 readings, by about what factor did the spread of single trials shrink?

   AAbout 17 times BAbout 10 times CAbout 9.5 times DAbout 170 times

10. Question 10 of 20 · Multiple Choice

    The video says the returning beam "came back a little off course, shifted by about 11 to 13 centimeters" (Source 4, paragraph 3). How does this compare with Source 1?

    AIt contradicts Source 1, which says the deflection was never more than 70 millimeters BIt fits Source 1, which planned 100 millimeters and reports 115 millimeters on April 2 CIt cannot be compared, because Source 1 gives the deflection in feet, not in millimeters DIt contradicts Source 1, which says the deflection was about 43 millimeters in the final series

11. Question 11 of 20 · Multiple Choice

    The video ends: "Today the speed of light is fixed by definition ... so there is nothing left to measure" (Source 4, paragraph 6). Which evaluation is best?

    AIt is false, because Source 5 gives a value that is only approximate BIt is fully accurate, because a value fixed by definition can never be tested by experiment CPartly right: the value is exact by definition, and timing light now fixes the meter DIt is false, because Source 3 shows that the speed of light depends on the observer

12. Question 12 of 20 · Multiple Choice

    A student needs the size of the correction from air to a vacuum. Which source should she use, and why?

    ASource 4, because the video gives the most recent account of the experiment BSource 2, part B, because the table lists the result of every group of observations CSource 1, because the Introduction describes the apparatus in the most detail DSource 3, because Michelson states the correction, +80 km/s, and how he found it

13. Question 13 of 20 · Multiple Choice

    Which set of sources is needed, and enough, to answer "Was Michelson's result correct within the error limit he stated?"

    ASource 3 for his value and limit, and Source 5 for the modern value BDiagram 1 alone, because it shows all 100 of his readings CSource 4 alone, because it states the answer directly DSource 1 and Source 2, part B, because they report his early and grouped results

14. Question 14 of 20 · Multiple Choice

    Source 3, paragraph 1, gives the limit of error as "±.00017" of the result. Which statement is correct?

    AIt is 0.17 percent, and it matches ±510 km/s BIt is 1.7 percent, and it matches ±5,100 km/s CIt is 0.0017 percent, and it matches ±5 km/s DIt is 0.017 percent, and it matches ±51 km/s

15. Question 15 of 20 · Short Answer

    Answer the lesson's question in one paragraph: How fast does light travel, and how far can we trust Michelson's 1880 answer? Integrate at least three sources, cite each, and include at least two numbers.

    Show model answer

16. Question 16 of 20 · Short Answer

    Evaluate the video (Source 4) as a source. Name two of its statements that are accurate and two that are misleading or false, other than those checked in Examples 3 and 4, and support each with a specific source. Then say what the video is and is not useful for.

    Show model answer

17. Question 17 of 20 · Short Answer

    Describe the shape and spread of Diagram 1 in words. Then explain what the spread of single readings, the "Average difference from mean" of 60 in Source 2, part B, and the error limit of ±51 in Source 3 each tell a reader, and why the mean can be far more precise than a single reading and still be wrong.

    Show model answer

18. Question 18 of 20 · Short Answer

    Redesign the video's bar chart (Source 4, paragraph 5) so that it shows the comparison honestly. Describe the chart type, the axis and what it marks, and explain how Diagram 2 does or does not already solve the problem.

    Show model answer

19. Question 19 of 20 · Short Answer

    Plan one new visual that integrates Diagram 1, Source 3 and Source 5 to answer the question "Was the error in Michelson's 1879 result random or systematic?" Describe what it shows and what a reader would conclude from it.

    Show model answer

20. Question 20 of 20 · Short Answer

    Michelson says his limit of ±51 km/s covers the case "where the errors are all in the same direction" (Source 3, paragraph 1). What does the comparison with Source 5 suggest about that limit, and what general lesson does it teach about evaluating even a careful primary source?

    Show model answer

These standards connect to RST.11-12.7: prerequisites to review first, parallel standards at the same level, and next steps that build on it.

Standard text: Common Core State Standards for English Language Arts & Literacy. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.