The equation of an electromagnetic wave is:

E = 2 sin(2×10¹⁵t − 10⁷x)

Find the refractive index of the medium.

Solution:

Comparing with:

E = E₀ sin(ωt − kx)

ω = 2×10¹⁵

k = 10⁷

Wave speed:

v = ω/k

= (2×10¹⁵)/(10⁷)

= 2×10⁸ m/s

Refractive index:

n = c/v

= (3×10⁸)/(2×10⁸)

= 3/2

Answer: 3/2