Physics · Ch 6 — Optics
Refractive Index
Refractive Index
The refractive index of a transparent medium is defined as the ratio of the speed of light in vacuum (or air) to the speed of light in that medium: . Refractive index has no unit (it is a pure ratio) and is always , equal to exactly 1 only for vacuum itself; it is sometimes called the optical density of the medium (not to be confused with ordinary mass density, an unrelated quantity) -- a higher refractive index always means a denser optical medium in which light travels correspondingly more slowly. Representative values: vacuum 1.00, air 1.0003, carbon dioxide gas 1.0005, ice 1.31, pure water 1.33, ethyl alcohol 1.36, quartz 1.46, glass 1.52, sapphire 1.77, diamond 2.42, gallium phosphide 3.50 (the highest listed). Because a light wave's frequency is fixed entirely by its source and does not change across media, while its speed does change, its wavelength must change too: $v=\nu\la …
| Media | Refractive index |
|---|---|
| Vacuum | 1.00 |
| Air | 1.0003 |
| Carbon dioxide gas | 1.0005 |
| Ice | 1.31 |
| Pure water | 1.33 |
| Ethyl alcohol | 1.36 |
| Quartz | 1.46 |
| Vegetable oil | 1.47 |
| Olive oil | 1.48 |
| Acrylic | 1.49 |
| Table salt | 1.51 |
| Glass | 1.52 |
| Sapphire | 1.77 |
| Zircon | 1.92 |
Worked out. Refractive index is defined as n = c/v, so the speed inside the medium is simply v = c/n. Substituting the given refractive index n = 1.5 and the standard vacuum speed c = 3 times 10 to the 8 metres per second gives v = (3 times 10 to the 8)/1.5 = 2 times 10 to the 8 metres per second. So light travels noticeably more slowly, at two-thirds its vacuum speed, once it enters this particular glass -- a direct numerical illustration of what the refractive index physically represents: the factor by which a medium slows li …
Worked out. Sodium light of vacuum wavelength 5893 angstrom enters water of refractive index 1.33. Using lambda-1/lambda-2 = n2/n1 with n1 = 1 (vacuum) and n2 = 1.33 gives the wavelength in water as lambda2 = 5893/1.33 = 4431 angstrom -- noticeably shorter than in vacuum. Using v = c/n gives the speed in water as v2 = (3 times 10 to the 8)/1.33 = 2.256 times 10 to the 8 metres per second, again slower than in vacuum. Finally, computing frequency two independent ways -- from v1 = c/lambda1 in vacuum, and separately from v2 = v2(speed)/lambda2 in water -- both give the same value, about 5.091 times 10 to the 14 hertz, confirming the general rule that a light wave's frequency is fixed by its source and stays exactly the same in every medium it passes through; only its wavelength and …