When sun light is scatterred by minute particles of atmosphere, then the intensity of light scattered away is proportional to

Options

A. `("wavelength of light")^(4)`
B. `("frequency of light")^(4)`
C. `("wavelength of light")^(2)`
D. `("frequency of light")^(2)`

Explanation

To solve the problem, we need to understand the relationship between the intensity of light scattered by minute particles in the atmosphere and the wavelength or frequency of the light.

### Step-by-Step Solution:

1. **Understanding Scattering**:
- Scattering occurs when light interacts with small particles in the atmosphere. The particles absorb the incoming light and then re-emit it in different directions.

2. **Rayleigh Scattering**:
- According to Rayleigh's scattering theory, the intensity of light scattered by small particles is inversely proportional to the fourth power of the wavelength (λ) of the light. This can be expressed mathematically as:
\[ I \propto \frac{1}{\lambda^4} \]
- This means that as the wavelength increases, the intensity of the scattered light decreases significantly.

3. **Relating Wavelength and Frequency**:
- The frequency (ν) of light is related to its wavelength by the equation:
\[ c = \lambda \cdot \nu \]
where \(c\) is the speed of light. From this, we can express wavelength in terms of frequency:
\[ \lambda = \frac{c}{\nu} \]
- Substituting this into the scattering equation gives:
\[ I \propto \frac{1}{\left(\frac{c}{\nu}\right)^4} = \frac{\nu^4}{c^4} \]
- Thus, we can also say that the intensity of scattered light is directly proportional to the fourth power of the frequency:
\[ I \propto \nu^4 \]

4. **Conclusion**:
- From the above analysis, we conclude that the intensity of light scattered away is proportional to the frequency raised to the power of 4. Therefore, the correct answer is:
\[ \text{Intensity of scattered light} \propto \text{frequency}^4 \]

### Final Answer:
The intensity of light scattered away is proportional to frequency to the power 4.