Question

The electric field of an electromagnetic wave travelling through a medium is given by \[ \vec{E}(x,t)=25\sin(2\times10^{15}t-10^{7}x)\,\hat{n}. \] Then the refractive index of the medium is ________. (All given measurements are in SI units)

• A. \(1.7\)
• B. \(1.5\)
• C. \(1.2\)
• D. \(2\)

Hint:

Always compare the given wave equation with \( \sin(\omega t-kx) \) to directly read \( \omega \) and \( k \).

Answer 1

The Correct Option is B

Concept: For a plane electromagnetic wave of the form \[ E=E_0\sin(\omega t-kx), \] the wave speed is given by \[ v=\frac{\omega}{k}. \] The refractive index \( n \) of the medium is: \[ n=\frac{c}{v} \] where \( c=3\times10^8 \, \text{m s}^{-1} \).
Step 1: Identify angular frequency and wave number From the given equation: \[ \omega = 2\times10^{15}\ \text{rad s}^{-1},\quad k = 10^{7}\ \text{m}^{-1} \]
Step 2: Calculate the wave speed in the medium \[ v=\frac{\omega}{k} =\frac{2\times10^{15}}{10^{7}} =2\times10^{8}\ \text{m s}^{-1} \]
Step 3: Find the refractive index \[ n=\frac{c}{v} =\frac{3\times10^{8}}{2\times10^{8}} =1.5 \]