In a medium, the electric field-in an EM wave is `E=E_(0) sin 12 xx 10^(6)(z-2 xx 10^((s)) t) (N) / (C)` The refractive index of the medium is

Answer

To find the refractive index of the medium from the given electric field of an electromagnetic wave, we can follow these steps:

### Step 1: Identify the wave equation parameters
The given electric field of the electromagnetic wave is:
\[ E = E_0 \sin(12 \times 10^6 (z - 2 \times 10^8 t)) \]

From the wave equation \( E = E_0 \sin(kz - \omega t) \), we can identify:
- \( k = 12 \times 10^6 \) (the wave number)
- \( \omega = 2 \times 10^8 \) (the angular frequency)

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

Substituting the values we identified:
\[ v = \frac{2 \times 10^8}{12 \times 10^6} \]

### Step 3: Simplify the calculation
Calculating the above expression:
\[ v = \frac{2}{12} \times 10^{8 - 6} = \frac{1}{6} \times 10^2 = \frac{100}{6} \approx 16.67 \, \text{m/s} \]

### Step 4: Use the speed of light to find the refractive index
The refractive index \( n \) of the medium is given by the ratio of the speed of light in vacuum \( c \) to the speed of the wave in the medium \( v \):
\[ n = \frac{c}{v} \]

Where \( c \approx 3 \times 10^8 \, \text{m/s} \). Substituting the values:
\[ n = \frac{3 \times 10^8}{16.67} \]

### Step 5: Calculate the refractive index
Calculating the above expression:
\[ n \approx \frac{3 \times 10^8}{16.67} \approx 1.8 \]

### Conclusion
The refractive index of the medium is approximately \( n \approx 1.8 \).

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