Which of the following statement (s) is/are correct?
I. A point source emitting waves uniformly in all directions.
II. In spherical wave, the locus of point which have the same amplitude and vibrate in same phase are spheres.
III. At a small distance from the source, a small portion of sphere can be considered as plane wave.

Options

A. Only I
B. Both I and II
C. Only III
D. All of these

Explanation

To determine which of the statements are correct, let's analyze each statement one by one.

### Step 1: Analyze Statement I
**Statement I:** A point source emitting waves uniformly in all directions.

- A point source emits waves in all directions uniformly. This is a fundamental characteristic of point sources in wave theory. The intensity of the waves decreases with distance, but the waves propagate equally in all directions. Therefore, this statement is **correct**.

### Step 2: Analyze Statement II
**Statement II:** In spherical wave, the locus of points which have the same amplitude and vibrate in the same phase are spheres.

- In wave theory, a wave front is defined as the locus of points that have the same phase of vibration. For spherical waves, these wave fronts are indeed spherical surfaces. Thus, this statement is also **correct**.

### Step 3: Analyze Statement III
**Statement III:** At a small distance from the source, a small portion of a sphere can be considered as a plane wave.

- For a wave to be approximated as a plane wave, the distance from the source must be large enough such that the curvature of the wave front is negligible. At small distances, the wave front is still significantly curved, and therefore, a small portion of the sphere cannot be considered flat. This statement is **incorrect**.

### Conclusion
- Statement I: Correct
- Statement II: Correct
- Statement III: Incorrect

Thus, the correct statements are I and II.

### Final Answer
The correct statements are I and II.

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