Question

A plane electromagnetic wave represented as \( E = 100 \cos (6 \times 10^8 t + 4x) \, \text{V/m} \), is propagated through a medium of refractive index:

• A. 1.5
• B. 2.0
• C. 2.4
• D. 4.0

Hint:

The refractive index of a medium can be calculated using the wave number and angular frequency, and it indicates how much the wave is slowed in the medium compared to vacuum.

Answer 1

The Correct Option is B

Step 1: Electromagnetic Wave Propagation.
The given wave equation for the electric field is in the form \( E = E_0 \cos(\omega t + kx) \), where \( E_0 \) is the amplitude, \( \omega \) is the angular frequency, and \( k \) is the wave number.

Step 2: Relating to Refractive Index.
The refractive index \( n \) of a medium is related to the speed of light in the medium and the speed of light in vacuum. It is given by: \[ n = \frac{c}{v} \] where \( c \) is the speed of light in a vacuum, and \( v \) is the speed of light in the medium. The wave number \( k \) is related to the speed of light in the medium by: \[ k = \frac{\omega}{v} \] By comparing the wave equation given, we find that the refractive index is \( n = 2.0 \).

Step 3: Conclusion.
Therefore, the refractive index is \( 2.0 \), making the correct answer (B).