In a Young's double slit experiment, films of thickness `t_(A)` and `t_(B)` and refcative indices `mu_(A)` and `mu_(B)` are placed in front of slits A and B respectively. If `mu_(A)t_(A)=mu_(B)t_(B)`, then the central maxima may

Options

A. not shift
B. shift towards A if `t_A lt t_B`
C. shift towards B if `t_Alt t_B`
D. shift towards A if `t_A gt t_B`

Answer

To solve the problem, we need to analyze the situation in a Young's double slit experiment with films of different thicknesses and refractive indices placed in front of the slits.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have two slits A and B, with films of thickness \( t_A \) and \( t_B \) and refractive indices \( \mu_A \) and \( \mu_B \) placed in front of each slit respectively.

2. **Path Difference Calculation**:
- The optical path length for light passing through a medium is given by the product of the refractive index and the thickness of the medium.
- For slit A, the optical path length is \( x_1 = t_A \mu_A \).
- For slit B, the optical path length is \( x_2 = t_B \mu_B \).

3. **Calculating the Shift**:
- The shift due to the films in front of the slits is given by:
\[ x = (t_A \mu_A - t_B \mu_B) + (t_B - t_A) \]
- This can be simplified to:
\[ x = (t_A \mu_A - t_B \mu_B) + t_B - t_A \]

4. **Using the Given Condition**:
- We are given that \( \mu_A t_A = \mu_B t_B \).
- This implies that \( t_A \mu_A - t_B \mu_B = 0 \).
- Therefore, substituting this into our equation for the shift:
\[ x = 0 + (t_B - t_A) = t_B - t_A \]

5. **Analyzing the Shift**:
- If \( t_B = t_A \), then \( x = 0 \); the central maxima does not shift.
- If \( t_B > t_A \), then \( x > 0 \); the central maxima shifts towards slit A.
- If \( t_B < t_A \), then \( x < 0 \); the central maxima shifts towards slit B.

### Conclusion:
- The central maxima will not shift if \( t_B = t_A \).
- The central maxima will shift towards A if \( t_B > t_A \).
- The central maxima will shift towards B if \( t_B < t_A \).

### Final Answer:
- The correct options are:
- Central maxima does not shift if \( t_B = t_A \).
- Central maxima shifts towards A if \( t_B > t_A \).
- Central maxima shifts towards B if \( t_B < t_A \).