Relation between electromagnetic waves and wave optics

Question

An Electromagnetic wave travelling through a transparent medium is given by E_{​​​​​​x} (y,t)=       E_{​​​​​​ox} sin2π [ (y/5×10^-7) - 3×10¹⁴ t ] in SI units. Then what is the refractive index of the medium?

Answer 1

An Electromagnetic wave travelling through a transparent medium is given by

E_{​​​​​​x} (y,t)=       E_{​​​​​​ox} sin2π [ (y/5×10^-7) - 3×10¹⁴ t ] in SI units

E_{​​​​​​x} (y,t)=       E_{​​​​​​ox} sin{2π/(/5×10^-7) ( y- 3×10¹⁴ x(5×10^-7)t )}

So velocity of the wave in the transparent medium will be

v = 3×10¹⁴ x(5×10^-7)=15×10⁷m/s

Again the velocity of electromagnetic wave in vacuum is c =3×10⁸ m/s

So refractive index of the medium u = c/v =( 3×10⁸ )/(15×10⁷)= 2