In Young's interference experiment, if the slit are of unequal width, then

Options

A. no fringe will be formed
B. the position of minimum intensity will not be completley dark
C. bright fringe as displaced form the original central position
D. distance between two consecutive dark fringe will not be equal to the distance between two consecutive brigth fringes

Explanation

To solve the question regarding Young's interference experiment with slits of unequal width, we will analyze the implications of having slits of different widths on the interference pattern.

### Step-by-Step Solution:

1. **Understanding Young's Experiment**:
In Young's double-slit experiment, two coherent light sources (or slits) produce an interference pattern on a screen due to the superposition of light waves.

2. **Effect of Unequal Widths**:
When the slits are of unequal width, the amplitude of the light waves emerging from each slit will be different. Let’s denote the amplitudes from slit S1 and S2 as A1 and A2 respectively, where A1 ≠ A2.

3. **Intensity Calculation**:
The intensity of light is proportional to the square of the amplitude. Therefore, the intensities from the two slits can be expressed as:
- Intensity from slit S1: \( I_1 \propto A_1^2 \)
- Intensity from slit S2: \( I_2 \propto A_2^2 \)

4. **Interference Pattern**:
The resultant intensity at any point on the screen due to interference can be calculated using the formula:
\[ I = I_1 + I_2 + 2\sqrt{I_1 I_2} \cos(\delta) \]
where \( \delta \) is the phase difference between the two waves.

5. **Minimum Intensity**:
The minimum intensity (destructive interference) occurs when \( \cos(\delta) = -1 \). However, since the amplitudes are unequal, the minimum intensity will not be zero. Instead, it will be:
\[ I_{\text{min}} = |I_1 - I_2| \]
This means that the dark fringes will not be completely dark.

6. **Position of Fringes**:
The positions of the bright and dark fringes are determined by the path difference and do not depend on the intensity of the light. Thus, the positions of the fringes remain unchanged despite the unequal widths of the slits.

7. **Fringe Width**:
The fringe width (distance between consecutive bright or dark fringes) is given by:
\[ \beta = \frac{\lambda D}{d} \]
where \( D \) is the distance from the slits to the screen and \( d \) is the distance between the slits. This remains constant and does not depend on the intensity of the light or the widths of the slits.

### Conclusion:
In Young's interference experiment with slits of unequal width, the following statements can be concluded:
- The minimum intensity will not be completely dark.
- The positions of the fringes will remain unchanged.
- The distances between consecutive dark and bright fringes will be equal.

Thus, the correct answer to the question is that the minimum intensity will not be completely dark.