Assertion: The pattern and position of fringes always remain same even after the introduction of transparent medium in a path of one of the slit.
Reason: The central fringe is bright or dark is depend upon the initial phase difference between the two coherence sources.

Explanation

To solve the assertion-reason question, we will analyze both the assertion and the reason step by step.

### Step 1: Understand the Assertion
The assertion states: "The pattern and position of fringes always remain the same even after the introduction of a transparent medium in the path of one of the slits."

- When a transparent medium is introduced in the path of one of the slits in a double-slit interference experiment, it changes the effective path length of the light coming from that slit. The effective path length can be calculated using the formula:
\[ \text{Effective Path Length} = t(\mu - 1) \]
where \( t \) is the thickness of the medium and \( \mu \) is the refractive index of the medium.

### Step 2: Analyze the Impact on Fringes
- The introduction of a transparent medium will cause a shift in the position of the fringes on the screen. Although the width of the fringes remains the same, the overall pattern is affected because the path difference changes.
- Therefore, the assertion that the pattern and position of fringes remain the same is **false**.

### Step 3: Understand the Reason
The reason states: "The central fringe is bright or dark depending upon the initial phase difference between the two coherent sources."

- The central fringe's brightness (whether it is bright or dark) indeed depends on the initial phase difference between the two coherent sources (the two slits). If the light waves from both slits arrive in phase at the center, a bright fringe is formed. If they arrive out of phase, a dark fringe is formed.
- Therefore, the reason is **true**.

### Conclusion
- The assertion is **false**.
- The reason is **true**.

Thus, the correct answer is that the assertion is false, and the reason is true.

### Final Answer
Assertion: False
Reason: True
Correct Option: 4

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