Statement I: Two coherent point sources of light having no-zero phase difference are separated by a small distance. Then, on the perpendicular bisector of line segment joining both the point sources, constructive interference cannot be obtained.
Statement II: For two waves from coherent point sources to interfere constructively at a point, the magnitude of their phase difference at that point must be `2 m pi` (where m is non-negative integer).

Options

A. Statement I is True, statement II is True, Statement II is a correct explanation for Statement I.
B. Statement I is True, Statement II is True, Statement II is NOT a correct explanation for Statement I.
C. Statement I is True, Statement II is False.
D. Statement I is False, Statement II is True.

Explanation

To analyze the statements provided in the question, we will break down each statement and evaluate its validity step by step.

### Step 1: Evaluate Statement I
**Statement I:** Two coherent point sources of light having non-zero phase difference are separated by a small distance. Then, on the perpendicular bisector of the line segment joining both the point sources, constructive interference cannot be obtained.

1. **Understanding Coherent Sources:** Coherent sources are sources that maintain a constant phase difference and have the same frequency.
2. **Perpendicular Bisector:** The perpendicular bisector of the line segment joining two sources is equidistant from both sources.
3. **Path Difference at the Bisector:** At any point on the perpendicular bisector, the path difference (Δx) between the waves from the two sources is zero because the distances to the point are equal.
4. **Phase Difference:** If there is a non-zero phase difference (let's denote it as φ), this phase difference can be expressed in terms of wavelength (λ). The condition for constructive interference is that the total phase difference must be an integer multiple of 2π (i.e., φ = 2mπ, where m is a non-negative integer).
5. **Conclusion for Statement I:** Even with a non-zero phase difference, if the initial phase difference is equal to nλ (where n is an integer), constructive interference can still occur. Therefore, the statement is **false**.

### Step 2: Evaluate Statement II
**Statement II:** For two waves from coherent point sources to interfere constructively at a point, the magnitude of their phase difference at that point must be 2mπ (where m is a non-negative integer).

1. **Condition for Constructive Interference:** For constructive interference to occur, the phase difference (φ) between the two waves must satisfy the condition φ = 2mπ.
2. **Understanding Intensity Expression:** The intensity of the resultant wave from two coherent sources can be expressed as:
\[ I = I_1 + I_2 + 2\sqrt{I_1 I_2} \cos(\phi) \]
Here, the intensity is maximum when cos(φ) = 1, which occurs when φ = 2mπ.
3. **Conclusion for Statement II:** Since the condition for maximum intensity (constructive interference) is indeed that the phase difference is an integer multiple of 2π, this statement is **true**.

### Final Conclusion
- **Statement I is false.**
- **Statement II is true.**
- Therefore, the correct option is that Statement 1 is false and Statement 2 is true.