The inverse square law of intensity (i.e., the intensity `prop1/r^2)` is valid for a

Options

A. 1.point source
B. 2.line source
C. 3.plane source
D. 4.cylindrical source.

Answer

To solve the question regarding the inverse square law of intensity, we need to analyze the different types of sources and how they emit light or energy. The question asks which type of source the inverse square law applies to: point source, line source, plane source, or cylindrical source.

### Step-by-Step Solution:

1. **Understanding Intensity**:
- Intensity (I) is defined as the power (P) per unit area (A). Mathematically, it can be expressed as:
\[ I = \frac{P}{A} \]

2. **Surface Area Consideration**:
- For a point source, the energy radiates uniformly in all directions, forming a sphere around the source. The surface area (A) of a sphere is given by:
\[ A = 4\pi r^2 \]
- Therefore, the intensity at a distance \( r \) from the point source can be expressed as:
\[ I = \frac{P}{4\pi r^2} \]
- This shows that intensity is inversely proportional to the square of the distance from the source, confirming the inverse square law.

3. **Analyzing Other Sources**:
- **Line Source**: A line source emits energy along a line. The intensity does not decrease with the square of the distance but rather depends on the geometry of the line, leading to a different relationship.
- **Plane Source**: A plane source emits energy uniformly over a plane. The intensity decreases with distance, but not according to the inverse square law.
- **Cylindrical Source**: Similar to the line source, a cylindrical source radiates energy in a cylindrical manner, which does not follow the inverse square law.

4. **Conclusion**:
- The inverse square law of intensity is valid only for a **point source**. This is because the energy spreads out uniformly in three-dimensional space, leading to the intensity being inversely proportional to the square of the distance from the source.

### Final Answer:
The inverse square law of intensity is valid for a **point source**.

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