What is the frequency of light that has a wavelength in water of `6.00xx10^(2)nm` if the refractive index for this light is `1.33` ?

Options

A. `3.76xx10^(14)Hz`
B. `6.65xx10^(14)Hz`
C. `5.00xx10^(14)Hz`
D. `7.25xx10^(14)Hz`

Answer

To find the frequency of light in water given its wavelength and the refractive index, we can follow these steps:

### Step-by-Step Solution:

1. **Convert Wavelength to Meters**:
The given wavelength in water is \( 6.00 \times 10^2 \) nm. We need to convert this to meters.
\[ \text{Wavelength in meters} = 6.00 \times 10^2 \, \text{nm} = 6.00 \times 10^2 \times 10^{-9} \, \text{m} = 6.00 \times 10^{-7} \, \text{m} \]

2. **Identify the Speed of Light in Water**:
The speed of light in a medium can be calculated using the formula:
\[ v = \frac{c}{n} \]
where \( c \) is the speed of light in vacuum (approximately \( 3.00 \times 10^8 \, \text{m/s} \)) and \( n \) is the refractive index of the medium. For water, \( n = 1.33 \).
\[ v = \frac{3.00 \times 10^8 \, \text{m/s}}{1.33} \approx 2.26 \times 10^8 \, \text{m/s} \]

3. **Calculate Frequency**:
The frequency \( f \) can be calculated using the formula:
\[ f = \frac{v}{\lambda} \]
where \( v \) is the speed of light in the medium and \( \lambda \) is the wavelength in the medium.
\[ f = \frac{2.26 \times 10^8 \, \text{m/s}}{6.00 \times 10^{-7} \, \text{m}} \approx 3.77 \times 10^{14} \, \text{Hz} \]

### Final Answer:
The frequency of light in water is approximately \( 3.77 \times 10^{14} \, \text{Hz} \).

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