A light wave has a frequency of `4xx10^(14)Hz` and a wavelength of `5xx10^(-7)` meters in a medium. The refractive index of the medium is

Options

A. 1.5
B. 1.33
C. 1.25
D. 1.7

Explanation

To find the refractive index of the medium, we can use the relationship between the speed of light in a medium, its frequency, and its wavelength. The refractive index (μ) is defined as the ratio of the speed of light in vacuum (c) to the speed of light in the medium (v).

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Frequency (f) = \(4 \times 10^{14} \text{ Hz}\)
- Wavelength (λ) = \(5 \times 10^{-7} \text{ m}\)
- Speed of light in vacuum (c) = \(3 \times 10^{8} \text{ m/s}\)

2. **Calculate the Speed of Light in the Medium (v):**
The speed of light in a medium can be calculated using the formula:
\[ v = f \cdot \lambda \]
Substituting the values:
\[ v = (4 \times 10^{14} \text{ Hz}) \cdot (5 \times 10^{-7} \text{ m}) = 2 \times 10^{8} \text{ m/s} \]

3. **Calculate the Refractive Index (μ):**
The refractive index is given by the formula:
\[ \mu = \frac{c}{v} \]
Substituting the values:
\[ \mu = \frac{3 \times 10^{8} \text{ m/s}}{2 \times 10^{8} \text{ m/s}} = 1.5 \]

4. **Conclusion:**
The refractive index of the medium is \(1.5\).

### Final Answer:
The refractive index of the medium is \(1.5\).

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