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The speed of light is now known to great precision. In fact, the speed of light in a vacuum c 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 × 10 8 m/s 3 . 00 × 10 8 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"} {}

where the approximate value of 3 . 00 × 10 8 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     n size 12{n} {} of a material to be

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

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

Value of the speed of light

c = 2 . 9972458 × 10 8 m/s 3 . 00 × 10 8 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"} {}

Index of refraction

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

That is, n 1 size 12{n>= 1} {} . [link] 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, n size 12{n} {} is close to 1.0. This seems reasonable, since atoms in gases are widely separated and light travels at c size 12{c} {} in the vacuum between atoms. It is common to take n = 1 size 12{n=1} {} for gases unless great precision is needed. Although the speed of light v size 12{v} {} in a medium varies considerably from its value c size 12{c} {} in a vacuum, it is still a large speed.

Index of refraction in various media
Medium n
Gases at 0ºC , 1 atm
Air 1.000293
Carbon dioxide 1.00045
Hydrogen 1.000139
Oxygen 1.000271
Liquids at 20ºC
Benzene 1.501
Carbon disulfide 1.628
Carbon tetrachloride 1.461
Ethanol 1.361
Glycerine 1.473
Water, fresh 1.333
Solids at 20ºC
Diamond 2.419
Fluorite 1.434
Glass, crown 1.52
Glass, flint 1.66
Ice at 20ºC 1.309
Polystyrene 1.49
Plexiglas 1.51
Quartz, crystalline 1.544
Quartz, fused 1.458
Sodium chloride 1.544
Zircon 1.923

Speed of light in matter

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

Strategy

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

Solution

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

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

The index of refraction for zircon is given as 1.923 in [link] , and c size 12{c} {} is given in the equation for speed of light. Entering these values in the last expression gives

v = 3 . 00 × 10 8 m/s 1 . 923 = 1.56 × 10 8 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" "." {}} } {}

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 [link] 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.

Law of refraction

[link] shows how a ray of light changes direction when it passes from one medium to another. As before, the angles are measured relative to a perpendicular to the surface at the point where the light ray crosses it. (Some of the incident light will be reflected from the surface, but for now we will concentrate on the light that is transmitted.) The change in direction of the light ray depends on how the speed of light changes. The change in the speed of light is related to the indices of refraction of the media involved. In the situations shown in [link] , medium 2 has a greater index of refraction than medium 1. This means that the speed of light is less in medium 2 than in medium 1. Note that as shown in [link] (a), the direction of the ray moves closer to the perpendicular when it slows down. Conversely, as shown in [link] (b), the direction of the ray moves away from the perpendicular when it speeds up. The path is exactly reversible. In both cases, you can imagine what happens by thinking about pushing a lawn mower from a footpath onto grass, and vice versa. Going from the footpath to grass, the front wheels are slowed and pulled to the side as shown. This is the same change in direction as for light when it goes from a fast medium to a slow one. When going from the grass to the footpath, the front wheels can move faster and the mower changes direction as shown. This, too, is the same change in direction as for light going from slow to fast.

Practice Key Terms 2

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Source:  OpenStax, Concepts of physics with linear momentum. OpenStax CNX. Aug 11, 2016 Download for free at http://legacy.cnx.org/content/col11960/1.9
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