Assertion: Distance between posittion of bright and dark fringe remain same in YDSE.
Reason: Fringe width `beta=(lamdaD)/(d)`.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reson are true but reason is not the correct explanation of assertion.
C. if assertion is true but reason is false.
D. If both assertion and reason are false.

Explanation

To solve the question, we need to analyze the assertion and the reason provided:

**Assertion**: The distance between the position of bright and dark fringes remains the same in Young's Double Slit Experiment (YDSE).

**Reason**: Fringe width \( \beta = \frac{\lambda D}{d} \).

### Step-by-Step Solution:

1. **Understanding the Setup of YDSE**:
- In the Young's Double Slit Experiment, light passes through two closely spaced slits and creates an interference pattern on a screen. This pattern consists of alternating bright and dark fringes.

2. **Identifying Bright and Dark Fringes**:
- Bright fringes (maxima) occur where constructive interference happens, and dark fringes (minima) occur where destructive interference happens.
- The positions of these fringes can be calculated based on the path difference between the light waves coming from the two slits.

3. **Fringe Width Definition**:
- The fringe width \( \beta \) is defined as the distance between two consecutive bright fringes (or two consecutive dark fringes). It is given by the formula:
\[ \beta = \frac{\lambda D}{d} \]
where:
- \( \lambda \) is the wavelength of the light,
- \( D \) is the distance from the slits to the screen,
- \( d \) is the distance between the two slits.

4. **Analyzing the Assertion**:
- The assertion states that the distance between the positions of bright and dark fringes remains the same. This is true because the fringe width \( \beta \) is constant for a given setup (fixed \( \lambda \), \( D \), and \( d \)).
- The distance between a bright fringe and the next dark fringe (or vice versa) is equal to \( \frac{\beta}{2} \), which remains constant.

5. **Analyzing the Reason**:
- The reason states the formula for fringe width \( \beta \). This formula is indeed correct and shows how fringe width is derived from the physical parameters of the experiment.
- Since \( \beta \) does not depend on the order of the fringe (whether it is the first, second, etc.), the distances between the fringes remain consistent.

6. **Conclusion**:
- Both the assertion and reason are true. The reason correctly explains why the assertion holds true.

### Final Answer:
The correct option is that both the assertion and reason are true, and the reason is the correct explanation of the assertion.