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. `1.33`

Answer

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

### Step 1: Identify the given values
- Frequency (F) = \(2 \times 10^{14} \text{ Hz}\)
- Wavelength (\(\lambda\)) = \(5000 \text{ Å}\)

### Step 2: Convert the wavelength from angstroms to meters
1 angstrom (Å) = \(10^{-10}\) meters, so:
\[ \lambda = 5000 \text{ Å} = 5000 \times 10^{-10} \text{ m} = 5 \times 10^{-7} \text{ m} \]

### Step 3: Calculate the speed of the light wave in the material
The speed of a wave (V) can be calculated using the formula:
\[ V = F \times \lambda \]
Substituting the values:
\[ V = (2 \times 10^{14} \text{ Hz}) \times (5 \times 10^{-7} \text{ m}) = 10 \times 10^{7} \text{ m/s} = 1 \times 10^{8} \text{ m/s} \]

### Step 4: Calculate the refractive index of the material
The refractive index (\(\mu\)) is given by the formula:
\[ \mu = \frac{C}{V} \]
Where \(C\) is the speed of light in vacuum, approximately \(3 \times 10^{8} \text{ m/s}\). Now substituting the values:
\[ \mu = \frac{3 \times 10^{8} \text{ m/s}}{1 \times 10^{8} \text{ m/s}} = 3 \]

### Final Answer
The refractive index of the material is \(3\).

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