Core Unit III: Light
A. Characteristics of Light

2. The Speed of Light

Key Concepts

Galileo's attempts to measure the speed of light were unsuccessful. The experimental design and technological restraints did not permit measurements of short time intervals to be made accurately.

Roemer's method, involving the careful observation of the eclipses of a moon of Jupiter (Io) at different times of the year, showed discrepancies in the duration of time prior to the start of the eclipse. Huygens interpreted these discrepancies as being due to the difference in the distance that light had to travel to reach the earth. He obtained a reasonable estimate for the speed of light. (Actually, Huygens' interpretation was not correct. It has also been suggested that he did not have the average diameter of the Earth's orbit around the sun to base his calculations on. The apparent differences in the time for the commencement of the eclipse is due to the relativistic motion between the Earth and Jupiter, depending on whether the Earth is moving towards or away from Jupiter in different parts of the Earth's orbit. Some physics texts oversimplify and misinterpret the explanation. However, the correct explanation goes beyond the scope of the course.)

Fizeau, Foucault, and Michelson were among the first to make reasonably accurate measurements of the speed of light using terrestrial methods.

Michelson's method involved a rotating octagonal mirror reflecting light to a concave mirror located about 35 km away. The light reflecting back from the concave mirror struck another face of the octagonal mirror, and could only be seen by an observer if the octagonal mirror was rotating at certain speeds. (To allow the mirror to make the minimum one-eighth rotation in the time it took the light to make the return trip required the octagonal mirror to make slightly more than 32 000 revolutions per minute.) From the round trip distance the light travelled, and the period of rotation of the octagonal mirror, the speed of light was determined.

Other recent experiments using more advanced technology have been used to measure the speed of light more accurately. The current accepted value for the speed of light can be approximated as 3.00 x 10⁸ m/s. (Where greater accuracy is required, c = 2.997 924 58 m/s.)

The speed of light in liquids and solids is significantly less than in a vacuum.

The ratio of the speed of light in a vacuum to the speed of light in a given material is called the absolute index of refraction n) of the material.

There are no units associated with the index of refraction.

The index of refraction in air is about 1.000 3. Light travels slightly slower in air than in a vacuum. Usually this discrepancy can be neglected, and the index of refraction of a material can be determined without having to take this into account.

The higher the index of refraction for a given material, the slower light travels through it.

The ratio of the absolute indices of refraction for light travelling from any medium to another is called the relative index of refraction.

One light year is the distance travelled by light in one year.

The astronomical unit, (A.U.), is the length of the semimajor axis of the Earth's orbit.

1 A.U. = 1.50 x 10¹¹ m.

The parsec, or parallax second, is the distance from the sun to a star such that it would have a parallax angle of one second of arc as viewed from the Earth.

1 parsec 3.09 x 10¹⁶ m, or 3.26 light years.

The astronomical unit and the parsec are non-SI units.

1 light year 9.44 x 10¹⁵ m

Learning Outcomes

Students will increase their abilities to:

1. Define the following terms: speed, absolute index of refraction, index of refraction, relative index of refraction, light year.

2. Describe the methods used by Galileo, Roemer, and Michelson to measure the speed of light.

3. Explain why the speed of light is difficult to measure.

4. State the value of the speed of light in a vacuum to three significant figures.

5. Explain that the speed of light is fastest in a vacuum and slower in other materials.

6. Recognize that the index of refraction for a particular medium can be used to determine the speed of light in that medium.

7. Apply the definition of the absolute index of refraction (or the definition of the index of refraction) to solve problems.

8. Explain that light travels slightly slower in air than in a vacuum, but in many situations this difference is negligible.

9. Recognize that the higher the value of the index of refraction for a particular medium the slower light will travel through that medium.

10. Solve problems to determine the relative index of refraction between any two given media.

11. Calculate the distance, in metres, that light travels in one light year, based on its speed in metres per second.

12. Explain why the light year is used to measure astronomical distances.

Teaching Suggestions, Activities and Demonstrations

1. Perform an activity, or use examples from common experience, to compare qualitatively the speeds of sound and light.

2. Explain why there are no units associated with an index of refraction. Show that if you tried to use units in the equation for the index of refraction, they would cancel out.

3. Apply the definition of a light year to convert distances from metres to light years (or vice versa).