The frequency of a light wave in a material is `2xx10^(14)Hz` and wavelength is `5000 Å`. The refractive index of material will be

Options

A. `1.40`
B. `1.50`
C. `3.00`
D. `1.33S`

Explanation

To find the refractive index of the material, we can follow these steps:

### Step 1: Identify the given values
We have:
- Frequency of the light wave, \( f = 2 \times 10^{14} \, \text{Hz} \)
- Wavelength of the light wave, \( \lambda = 5000 \, \text{Å} = 5000 \times 10^{-10} \, \text{m} = 5 \times 10^{-7} \, \text{m} \)

### Step 2: Calculate the speed of light in the material
The speed of light in a medium can be calculated using the formula:
\[ V = \lambda f \]
Substituting the values:
\[ V = (5 \times 10^{-7} \, \text{m})(2 \times 10^{14} \, \text{Hz}) \]
Calculating this gives:
\[ V = 10 \times 10^{7} \, \text{m/s} = 1 \times 10^{8} \, \text{m/s} \]

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

### Step 4: Substitute the values into the refractive index formula
Substituting the values we have:
\[ \mu = \frac{3 \times 10^{8} \, \text{m/s}}{1 \times 10^{8} \, \text{m/s}} \]
Calculating this gives:
\[ \mu = 3 \]

### Conclusion
The refractive index of the material is \( \mu = 3 \).

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