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9.3 The law of refraction  (Page 2/7)

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In stage one of the figure, the light falling from a source on an eight-sided mirror is viewed by an observer; in stage two, the mirror is made to rotate and the reflected light falling onto a stationary mirror kept at a certain distance of 35 kilometers is viewed by an observer. In stage three, the observer can see the reflected ray only when the mirror has rotated into the correct position just as the ray returns.
A schematic of early apparatus used by Michelson and others to determine the speed of light. As the mirrors rotate, the reflected ray is only briefly directed at the stationary mirror. The returning ray will be reflected into the observer's eye only if the next mirror has rotated into the correct position just as the ray returns. By measuring the correct rotation rate, the time for the round trip can be measured and the speed of light calculated. Michelson’s calculated value of the speed of light was only 0.04% different from the value used today.

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.

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Source:  OpenStax, General physics ii phy2202ca. OpenStax CNX. Jul 05, 2013 Download for free at http://legacy.cnx.org/content/col11538/1.2
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