Due to a point source of radiation, intensify is proportional to

Options

A. `("amplitude")^(2)`
B. `("amplitude")^(2)`
C. `("amplitude")^(4)`
D. `("amplitude")^(5)`

Answer

To solve the question, we need to understand how the intensity of radiation emitted by a point source is related to its amplitude. Here’s a step-by-step breakdown of the solution:

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

### Step 2: Characteristics of a Point Source
- **Point Source**: A point source of radiation emits energy uniformly in all directions. As the distance from the source increases, the energy spreads over a larger area.

### Step 3: Area of a Sphere
- **Surface Area Calculation**: The area (A) over which the radiation is spread at a distance (r) from the point source is the surface area of a sphere:
\[ A = 4\pi r^2 \]

### Step 4: Relation Between Intensity and Amplitude
- **Amplitude and Intensity**: The intensity of radiation is proportional to the square of the amplitude (A) of the wave. This relationship can be expressed as:
\[ I \propto A^2 \]
This means that if the amplitude doubles, the intensity increases by a factor of four (since \(2^2 = 4\)).

### Step 5: Conclusion
- **Final Answer**: Therefore, the intensity of radiation from a point source is proportional to the square of the amplitude. Hence, the correct answer to the question is:
\[ I \propto A^2 \]