Find the ratio of frequencies of light waves of wavelengths 4000 A and 8000 A.

Answer

To find the ratio of frequencies of light waves with wavelengths of 4000 Å and 8000 Å, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Wavelengths**:
- Let \( \lambda_1 = 4000 \, \text{Å} \)
- Let \( \lambda_2 = 8000 \, \text{Å} \)

2. **Use the Relationship Between Frequency and Wavelength**:
- The frequency \( \nu \) of a wave is related to its wavelength \( \lambda \) by the equation:
\[ \nu = \frac{c}{\lambda} \]
where \( c \) is the speed of light.

3. **Calculate the Frequencies**:
- For \( \lambda_1 \):
\[ \nu_1 = \frac{c}{\lambda_1} = \frac{c}{4000 \, \text{Å}} \]
- For \( \lambda_2 \):
\[ \nu_2 = \frac{c}{\lambda_2} = \frac{c}{8000 \, \text{Å}} \]

4. **Find the Ratio of Frequencies**:
- The ratio of the frequencies \( \frac{\nu_1}{\nu_2} \) can be expressed as:
\[ \frac{\nu_1}{\nu_2} = \frac{c/\lambda_1}{c/\lambda_2} = \frac{\lambda_2}{\lambda_1} \]
- Substituting the values of \( \lambda_1 \) and \( \lambda_2 \):
\[ \frac{\nu_1}{\nu_2} = \frac{8000 \, \text{Å}}{4000 \, \text{Å}} = 2 \]

5. **Express the Ratio**:
- Therefore, the ratio of frequencies \( \nu_1 : \nu_2 \) is:
\[ \nu_1 : \nu_2 = 2 : 1 \]

### Final Answer:
The ratio of frequencies of light waves of wavelengths 4000 Å and 8000 Å is \( 2 : 1 \).

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