Early attempts to measure the speed of light, such as those made by Galileo, determined that light moved extremely fast, perhaps instantaneously. The first real evidence that light traveled at a finite speed came from the Danish astronomer Ole Roemer in the late 17th century. Roemer had noted that the average orbital period of one of Jupiter’s moons, as measured from Earth, varied depending on whether Earth was moving toward or away from Jupiter. He correctly concluded that the apparent change in period was due to the change in distance between Earth and Jupiter and the time it took light to travel this distance. From his 1676 data, a value of the speed of light was calculated to be 2.26×108 m/s2.26×108 m/s size 12{2 "." "26"´"10" rSup { size 8{8} } " m/s"} {} (only 25% different from today’s accepted value). In more recent times, physicists have measured the speed of light in numerous ways and with increasing accuracy. One particularly direct method, used in 1887 by the American physicist Albert Michelson (1852–1931), is illustrated in Figure 2. Light reflected from a rotating set of mirrors was reflected from a stationary mirror 35 km away and returned to the rotating mirrors. The time for the light to travel can be determined by how fast the mirrors must rotate for the light to be returned to the observer’s eye.

The speed of light is now known to great precision. In fact, the speed of light in a vacuum cc size 12{c} {} is so important that it is accepted as one of the basic physical quantities and has the fixed value

c=2.9972458×108 m/s≈3.00×108 m/s,c=2.9972458×108 m/s≈3.00×108 m/s, size 12{c=2 "." "9972458" times "10" rSup { size 8{8} } " m/s" approx 3 "." "00" times "10" rSup { size 8{8} } " m/s"} {}

(1)where the approximate value of 3.00×108 m/s3.00×108 m/s size 12{3 "." "00"´"10" rSup { size 8{8} } " m/s"} {} is used whenever three-digit accuracy is sufficient. The speed of light through matter is less than it is in a vacuum, because light interacts with atoms in a material. The speed of light depends strongly on the type of material, since its interaction with different atoms, crystal lattices, and other substructures varies. We define the index of refraction nn size 12{n} {} of a material to be

n=cv,n=cv, size 12{n= { {c} over {v} } } {}

(2)where vv size 12{v} {} is the observed speed of light in the material. Since the speed of light is always less than cc size 12{c} {} in matter and equals cc size 12{c} {} only in a vacuum, the index of refraction is always greater than or equal to one.

c=2.9972458×108 m/s≈3.00×108 m/sc=2.9972458×108 m/s≈3.00×108 m/s size 12{c=2 "." "9972458" times "10" rSup { size 8{8} } " m/s" approx 3 "." "00" times "10" rSup { size 8{8} } " m/s"} {}

(3)
n=cvn=cv size 12{n= { {c} over {v} } } {}

(4) That is, n≥1n≥1 size 12{n >= 1} {}. Table 1 gives the indices of refraction for some representative substances. The values are listed for a particular wavelength of light, because they vary slightly with wavelength. (This can have important effects, such as colors produced by a prism.) Note that for gases, nn size 12{n} {} is close to 1.0. This seems reasonable, since atoms in gases are widely separated and light travels at cc size 12{c} {} in the vacuum between atoms. It is common to take n=1n=1 size 12{n=1} {} for gases unless great precision is needed. Although the speed of light vv size 12{v} {} in a medium varies considerably from its value cc size 12{c} {} in a vacuum, it is still a large speed.

Table 1: **Index of Refraction in Various Media**
Medium |
*n* |

*Gases at 0ºC0ºC, 1 atm* |

Air |
1.000293 |

Carbon dioxide |
1.00045 |

Hydrogen |
1.000139 |

Oxygen |
1.000271 |

*Liquids at 20ºC20ºC * |

Benzene |
1.501 |

Carbon disulfide |
1.628 |

Carbon tetrachloride |
1.461 |

Ethanol |
1.361 |

Glycerine |
1.473 |

Water, fresh |
1.333 |

*Solids at 20ºC20ºC* |

Diamond |
2.419 |

Fluorite |
1.434 |

Glass, crown |
1.52 |

Glass, flint |
1.66 |

Ice at 20ºC20ºC |
1.309 |

Polystyrene |
1.49 |

Plexiglas |
1.51 |

Quartz, crystalline |
1.544 |

Quartz, fused |
1.458 |

Sodium chloride |
1.544 |

Zircon |
1.923 |

Calculate the speed of light in zircon, a material used in jewelry to imitate diamond.

*Strategy*

The speed of light in a material, vv size 12{v} {}, can be calculated from the index of refraction nn size 12{n} {} of the material using the equation n=c/vn=c/v size 12{n=c/2} {}.

*Solution*

The equation for index of refraction states that n=c/vn=c/v size 12{n=c/v} {}. Rearranging this to determine vv size 12{v} {} gives

v=cn.v=cn. size 12{v= { {c} over {n} } } {}

(5)The index of refraction for zircon is given as 1.923 in Table 1, and cc size 12{c} {} is given in the equation for speed of light. Entering these values in the last expression gives

v
=
3.00×108 m/s1.923
=
1.56×108 m/s.
v
=
3.00×108 m/s1.923
=
1.56×108 m/s.
alignl { stack {
size 12{v= { {3 "." "00"´"10" rSup { size 8{8} } " m/s"} over {1 "." "923"} } } {} #
=1 "." "56"´"10" rSup { size 8{8} } " m/s" "." {}
} } {}

(6)*Discussion*

This speed is slightly larger than half the speed of light in a vacuum and is still high compared with speeds we normally experience. The only substance listed in Table 1 that has a greater index of refraction than zircon is diamond. We shall see later that the large index of refraction for zircon makes it sparkle more than glass, but less than diamond.

Comments:"This introductory, algebra-based, two-semester college physics book is grounded with real-world examples, illustrations, and explanations to help students grasp key, fundamental physics concepts. […]"