Choose the incorrect statements.

Options

A. A. An electron beam is used to obtain interference in a simple Young's double-slit experiment . If speed of electron is increased the fringe width decreases.
B. B. de-Broglie wavelength of electron is inversely proportional to the speed of electrons.
C. C. Two coherent point sources of light having non-zero phase difference are separated by a small distance. On the perpendicular bisector of line segment joining both the point sources, no constructive interference can be obtained
D. D. For two waves from coherent point sources to interference constructively at a point the magnitude of their phase difference at that point must be `2npi` (where n is non-negative integer)

Explanation

To solve the question of identifying the incorrect statements regarding interference in physics, we will analyze each statement step by step.

### Step-by-Step Solution:

1. **Statement A**: "An electron beam is used to obtain interference in simple Young's double slit experiment. If the speed of the electron is increased, the fringe width decreases."
- **Analysis**: The fringe width (β) in Young's double slit experiment is given by the formula:
\[ \beta = \frac{\lambda D}{d} \]
where \( \lambda \) is the wavelength, \( D \) is the distance from the slits to the screen, and \( d \) is the distance between the slits. The de Broglie wavelength of an electron is given by:
\[ \lambda = \frac{h}{mv} \]
where \( h \) is Planck's constant, \( m \) is the mass of the electron, and \( v \) is its velocity. As the speed \( v \) increases, the wavelength \( \lambda \) decreases, leading to a decrease in fringe width \( \beta \). Thus, this statement is **correct**.

2. **Statement B**: "De Broglie wavelength of an electron is inversely proportional to speed of electron."
- **Analysis**: From the de Broglie wavelength formula:
\[ \lambda = \frac{h}{mv} \]
it is clear that as the speed \( v \) increases, the wavelength \( \lambda \) decreases, confirming that the wavelength is indeed inversely proportional to the speed of the electron. Therefore, this statement is also **correct**.

3. **Statement C**: "Two coherent point sources of light having non-zero phase difference are separated by a small distance on the perpendicular bisector of the line segment joining both point sources; no constructive interference can be obtained."
- **Analysis**: For constructive interference to occur, the phase difference \( \Delta \phi \) must be an integer multiple of \( 2\pi \) (i.e., \( \Delta \phi = 2n\pi \)). Even if there is a non-zero phase difference, constructive interference can still occur if the path difference corresponds to \( n\lambda \). Therefore, this statement is **incorrect**.

4. **Statement D**: "For two waves from coherent point sources to interfere constructively at a point, the magnitude of their phase difference at that point must be \( 2n\pi \)."
- **Analysis**: This statement is true as it aligns with the condition for constructive interference. Therefore, this statement is **correct**.

### Conclusion:
The incorrect statement is **C**.