If a is the size of scatterer and `lamda` is the wavelength of light then Rayleigh law of scattering is valid for

Options

A. `a=lamda`
B. `agtgtlamda`
C. `a=lamda//2`
D. `altltlamda`

Answer

To determine the conditions under which Rayleigh's law of scattering is valid, we need to analyze the relationship between the size of the scatterer (denoted as 'a') and the wavelength of light (denoted as 'λ').

### Step-by-Step Solution:

1. **Understanding Rayleigh's Law of Scattering**:
Rayleigh's law states that the amount of scattering is inversely proportional to the fourth power of the wavelength of light. This means that shorter wavelengths (like violet light) scatter more than longer wavelengths (like red light).

2. **Condition for Validity**:
For Rayleigh's law to be applicable, the size of the scatterer (a) must be much smaller than the wavelength of light (λ). Mathematically, this is expressed as:
\[ a \ll \lambda \]
This means that the size of the scatterer should be significantly less than the wavelength of light.

3. **Examples of Scatterers**:
Common scatterers in the atmosphere include water droplets, air particles, and dust particles. When these particles are much smaller than the wavelength of visible light, Rayleigh's law can be applied.

4. **Consequences of the Condition**:
When the size of the scatterer is much smaller than the wavelength, different wavelengths of light scatter differently. For example, blue light (shorter wavelength) scatters more than red light (longer wavelength), which is why the sky appears blue.

5. **When Rayleigh's Law Fails**:
If the size of the scatterer is approximately equal to the wavelength of light (a ≈ λ), Rayleigh's law does not hold. In this case, all wavelengths scatter equally, leading to phenomena such as clouds appearing white.

### Conclusion:
Rayleigh's law of scattering is valid when the size of the scatterer (a) is much smaller than the wavelength of light (λ), specifically when:
\[ a \ll \lambda \]