Find the range of frequency of light that is visible to an average human being `(400nmltlamdalt700nm)`

Explanation

To find the range of frequency of light that is visible to an average human being, we will use the relationship between the speed of light, wavelength, and frequency. The formula we will use is:

\[ v = \lambda \cdot f \]

Where:
- \( v \) is the speed of light (approximately \( 3 \times 10^8 \) m/s),
- \( \lambda \) is the wavelength (in meters),
- \( f \) is the frequency (in hertz).

### Step-by-Step Solution

1. **Convert Wavelengths from Nanometers to Meters**:
- The visible light range is given as \( 400 \, \text{nm} \) to \( 700 \, \text{nm} \).
- Convert these values to meters:
\[ \lambda_1 = 400 \, \text{nm} = 400 \times 10^{-9} \, \text{m} \]
\[ \lambda_2 = 700 \, \text{nm} = 700 \times 10^{-9} \, \text{m} \]

2. **Calculate Frequency for \( \lambda_1 \)**:
- Use the formula \( f = \frac{v}{\lambda} \) for \( \lambda_1 \):
\[ f_1 = \frac{v}{\lambda_1} = \frac{3 \times 10^8 \, \text{m/s}}{400 \times 10^{-9} \, \text{m}} \]
- Calculate \( f_1 \):
\[ f_1 = \frac{3 \times 10^8}{400 \times 10^{-9}} = \frac{3 \times 10^8}{4 \times 10^{-7}} = 7.5 \times 10^{14} \, \text{Hz} \]

3. **Calculate Frequency for \( \lambda_2 \)**:
- Use the same formula for \( \lambda_2 \):
\[ f_2 = \frac{v}{\lambda_2} = \frac{3 \times 10^8 \, \text{m/s}}{700 \times 10^{-9} \, \text{m}} \]
- Calculate \( f_2 \):
\[ f_2 = \frac{3 \times 10^8}{700 \times 10^{-9}} = \frac{3 \times 10^8}{7 \times 10^{-7}} \approx 4.2857 \times 10^{14} \, \text{Hz} \]

4. **Determine the Range of Frequencies**:
- The range of frequencies visible to an average human being is from \( f_2 \) to \( f_1 \):
\[ \text{Range} = [4.2857 \times 10^{14} \, \text{Hz}, 7.5 \times 10^{14} \, \text{Hz}] \]

### Final Answer
The range of frequency of light that is visible to an average human being is approximately:
\[ 4.2857 \times 10^{14} \, \text{Hz} \text{ to } 7.5 \times 10^{14} \, \text{Hz} \]