A plane electromagnetic wave
`F_(s)=100 cos(6xx10^(8)t+4x) V//m` propagates in a medium of dielectric constant. The refractive index is

Options

A. `1.5`
B. `2.0`
C. `2.4`
D. `4.0`

Explanation

To find the refractive index of the medium in which the electromagnetic wave is propagating, we can follow these steps:

### Step 1: Identify the wave equation parameters
The given electromagnetic wave is represented as:
\[ F_s = 100 \cos(6 \times 10^8 t + 4x) \, \text{V/m} \]

From this equation, we can identify:
- The angular frequency \( \omega \) is \( 6 \times 10^8 \, \text{rad/s} \).
- The wave number \( k \) is \( 4 \, \text{rad/m} \).

### Step 2: Calculate the speed of the wave in the medium
The speed of the wave \( v \) in the medium can be calculated using the relationship between \( \omega \) and \( k \):
\[ v = \frac{\omega}{k} \]

Substituting the values:
\[ v = \frac{6 \times 10^8}{4} = 1.5 \times 10^8 \, \text{m/s} \]

### Step 3: Calculate the refractive index
The refractive index \( n \) of the medium is given by the formula:
\[ n = \frac{c}{v} \]
where \( c \) is the speed of light in vacuum, approximately \( 3 \times 10^8 \, \text{m/s} \).

Substituting the values:
\[ n = \frac{3 \times 10^8}{1.5 \times 10^8} = 2 \]

### Final Answer
Thus, the refractive index of the medium is:
\[ n = 2 \]

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