For a wavelength of light and scattering object is size a, all wavelengths are scattered nearly equally, if:

Options

A. a=1
B. `a gt gt 1`
C. `a lt lt 1`
D. `a^(3)I`

Answer

To solve the question, we need to analyze the conditions under which all wavelengths of light are scattered nearly equally by an object of size \( a \).

### Step-by-Step Solution:

1. **Understanding Scattering**: Scattering occurs when light interacts with particles or objects. The extent and nature of scattering depend on the size of the scattering object relative to the wavelength of light.

2. **Identify the Relationship**: For scattering to be nearly equal for all wavelengths, the size of the scattering object \( a \) must be compared to the wavelength \( \lambda \) of the light.

3. **Condition for Equal Scattering**:
- If the size of the object \( a \) is much larger than the wavelength \( \lambda \) (i.e., \( a \gg \lambda \)), then the scattering becomes independent of the wavelength. This is because the object behaves like a geometric obstacle to the light.
- Conversely, if the size of the object is comparable to or smaller than the wavelength, the scattering characteristics will vary significantly with wavelength.

4. **Conclusion**: Therefore, for all wavelengths to be scattered nearly equally, the size of the scattering object \( a \) should be much greater than 1 (in units of the wavelength). This leads us to conclude that the correct option is:
- **Option B**: \( a \gg 1 \)

### Final Answer:
The correct condition is that \( a \) should be greater than \( \lambda \) (or \( a \gg 1 \)) for all wavelengths to be scattered nearly equally.