In a Young's double slit experiment, the angular separation of the interference fringes on a distance screen is `0.04A^(0)`. The angular separation if the entire apparatus is immersed in a liquid of R.I. `4/3` is `0.0nA^(0)`, then what is the value of `n`?

Explanation

To solve the problem, we need to understand the relationship between the angular separation of the interference fringes in a Young's double slit experiment and the refractive index of the medium in which the apparatus is placed.

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Angular separation in air (α_A) = 0.04 A°.
- Refractive index of the liquid (μ) = 4/3.
- Angular separation in the liquid (α_L) = 0.0 n A°.

2. **Understand the Relationship**:
The angular separation (α) is directly proportional to the wavelength (λ) of the light used. When the apparatus is immersed in a medium with a refractive index, the wavelength of light changes according to the formula:
\[ \lambda_L = \frac{\lambda_A}{\mu} \]
where:
- λ_A = wavelength in air,
- λ_L = wavelength in the liquid,
- μ = refractive index of the liquid.

3. **Relate Angular Separations**:
The angular separations in air and liquid can be related as follows:
\[ \frac{\alpha_A}{\alpha_L} = \frac{\lambda_A}{\lambda_L} \]
Substituting the expression for λ_L:
\[ \frac{\alpha_A}{\alpha_L} = \frac{\lambda_A}{\frac{\lambda_A}{\mu}} = \mu \]

4. **Substituting Known Values**:
Now substituting the known values into the equation:
\[ \frac{0.04}{0.0 n} = \frac{4}{3} \]

5. **Cross-Multiplying**:
Cross-multiplying gives:
\[ 0.04 \cdot 3 = 0.0 n \cdot 4 \]
Simplifying this:
\[ 0.12 = 0.0 n \cdot 4 \]

6. **Solving for n**:
Dividing both sides by 4:
\[ n = \frac{0.12}{4} = 0.03 \]

7. **Final Calculation**:
Since we have \(0.0 n\) in the angular separation, we can express n as:
\[ n = \frac{0.12}{4} = 0.03 \text{ (but we need to express it in terms of a whole number)} \]
To express it in terms of a whole number, we can multiply both sides by 100:
\[ n = \frac{12}{4} = 3 \]

### Conclusion:
Thus, the value of \(n\) is **3**.