The electric field of an electromagnetic wave travelling through a medium is given by E (x, t)=25 (2.0 10¹⁵ t-10⁷ x ) n then the refractive index of the medium is _ _ _ _ . (All given measurement are in SI units)

Step-by-step solution

The electric field is E(x,t) = 25 (2.0 10¹⁵t - 10^7 x) V/m. This is in the standard form E = E₀ ( t - kx) where angular frequency = 2.0 10¹⁵ rad/s and wave number k = 10^7 rad/m. The speed of the wave in the medium is v = k = 2.0 10¹⁵ 10^7 = 2.0 10^8 m/s. The refractive index is defined as n = c v where c = 3.0 10^8 m/s is the speed of light in vacuum. Therefore, n = 3.0 10^8 2.0 10^8 = 1.5