Inside a transparent medium a harmonic light wave is described by E(x,t) = 3.0 !…

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Wave propagation and light in media · Wave propagation and light in media

Optics and Photonics, Ch Harmonic waves, phasors and group velocity

Problem

Inside a transparent medium a harmonic light wave is described by

E(x,t) = 3.0\cos\!\left(1.57\times10^{7}\,x - 3.14\times10^{15}\,t\right)

with

x

in metres,

t

in seconds and

E

in volts per metre. Take the speed of light in vacuum as

c = 3.00\times10^{8}\ \mathrm{m\,s^{-1}}

; the frequency of the wave is set by its source and does not change when the light enters the medium. Find: ((a)) the wavelength of the wave inside the medium, in nm; ((b)) its frequency

\nu

, in Hz; ((c)) its phase velocity

v

, in

\mathrm{m\,s^{-1}}

; ((d)) the vacuum wavelength of the same light, in nm.

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