A place 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`

Answer

To solve the problem, we will follow these steps:

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

### Step 2: Compare with the standard form of the wave equation
The standard form of a plane electromagnetic wave is:
\[ E(z) = E_0 \cos(\omega t + kx) \]
From the given equation, we can identify:
- \(\omega = 6 \times 10^8 \, \text{rad/s}\)
- \(k = 4 \, \text{rad/m}\)

### Step 3: Calculate the phase velocity (V)
The phase velocity \(V\) of the wave is given by:
\[ V = \frac{\omega}{k} \]
Substituting the values of \(\omega\) and \(k\):
\[ V = \frac{6 \times 10^8}{4} = 1.5 \times 10^8 \, \text{m/s} \]

### Step 4: Use the refractive index formula
The refractive index \(n\) of a medium is given by:
\[ n = \frac{c}{V} \]
where \(c\) is the speed of light in vacuum, approximately \(3 \times 10^8 \, \text{m/s}\).

### Step 5: Substitute the values to find the refractive index
Now substituting the values of \(c\) and \(V\):
\[ n = \frac{3 \times 10^8}{1.5 \times 10^8} \]
Calculating this gives:
\[ n = 2 \]

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

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