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| The sign convention for the distance-dependent term of a wave | Parent topic |
A time-dependent monochromatic travelling-wave solution of the Maxwell equations at a fixed position in space, z, along the direction of travel (which I set to 0 for simplicity), can be written as follows:
| E(z = 0, t) = E0 exp(ωt) | (1) |
where t denotes time. In a medium where the wave travels at a constant velocity, v, the amplitude E(z', t') at another position, z' > z, should be the same as that at z at an earlier time t = t' - (z' - z) / v = t' - z' / v, since z = 0. Hence:
| E(z', t') | = E0 exp(ωt) | |
| = E0 exp(ωt' - z' ω / v) | ||
| = E0 exp(ωt' - z' 2π / λ) | ||
| = E0 exp(ωt' - z' k) | (2) |
where k is the wavenumber. It follows that if the time-dependent form of the wave amplitude is chosen to be exp(-ωt), then the space dependent term needs to be written as exp(+kz). I dropped the primes because I do not need anymore to refer to an erlier time and position of the wave. This sign rule has direct implications for the sign of the refractive index.
| CITATION: Jonasz M. 2006. Refractive index (www.tpdsci.com/Tpc/RI.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published: 30-Oct-2006 Modified: 30-Oct-2006 Peer-reviewed: PENDING |
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