Q. The electric field of an electromagnetic wave travelling through a medium is given by

E(x, t) = 25 sin (2.0 × 10¹⁵ t − 10⁷ x) n̂

then the refractive index of the medium is ______.

(All given measurement are in SI units)

(A) 2

(B) 1.2

(C) 1.5

(D) 1.7

Correct Answer: 1.5

Explanation

The standard equation of an electromagnetic wave is:

E(x, t) = E₀ sin (ωt − kx)

Comparing it with the given equation:

ω = 2.0 × 10¹⁵ rad s⁻¹
k = 10⁷ m⁻¹

The speed of the electromagnetic wave in the medium is:

v = ω / k

v = (2.0 × 10¹⁵) / (10⁷) = 2.0 × 10⁸ m s⁻¹

Refractive index of the medium is given by:

n = c / v

n = (3.0 × 10⁸) / (2.0 × 10⁸) = 1.5

Hence, the refractive index of the medium is:

1.5

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