The electric field of an electromagnetic wave travelling through a medium is given by $\vec{E}(x, t)

Question

The electric field of an electromagnetic wave travelling through a medium is given by $\vec{E}(x, t)=25 \sin \left(2.0 	imes 10^{15} t-10^7 xight) \hat{n}$ then the refractive index of the medium is $\_\_\_\_$ .
(All given measurement are in SI units)

Professor PC Thomas Classes · Answer

Comparing the given equation with the standard wave equation $E = E_0 \sin(\omega t - kx)$, we have the angular frequency $\omega = 2.0 	imes 10^{15}$ rad/s and the wave number $k = 10^7$ m$^{-1}$. The speed of the wave in the medium is $v = \frac{\omega}{k} = \frac{2.0 	imes 10^{15}}{10^7} = 2.0 	imes 10^8$ m/s. The refractive index of the medium is $n = \frac{c}{v} = \frac{3 	imes 10^8}{2.0 	imes 10^8} = 1.5$.