To analyze the given statements, we will evaluate each one based on the principles of wave optics, specifically focusing on Young's Double Slit Experiment (YDSE) and the behavior of light.
### Step-by-Step Solution:
**Step 1: Evaluate Statement 1**
- **Statement**: In YDSE, if the initial phase difference between waves is `pi`, the central maxima will be occupied by minima.
- **Analysis**: The phase difference (Δφ) is given as π. The condition for minima in YDSE is that the path difference (Δx) must be an odd multiple of λ/2. The relationship between phase difference and path difference is given by:
\[
\Delta \phi = \frac{2\pi}{\lambda} \Delta x
\]
Setting Δφ = π, we can solve for Δx:
\[
\pi = \frac{2\pi}{\lambda} \Delta x \implies \Delta x = \frac{\lambda}{2}
\]
Since λ/2 is not an integral multiple of λ, the central point (where path difference is zero) will indeed be a minima. Thus, **Statement 1 is True**.
**Step 2: Evaluate Statement 2**
- **Statement**: In YDSE, if incident light is white light, then the central fringe is white while all other fringes are colored.
- **Analysis**: White light consists of multiple wavelengths (colors). At the center (where path difference is zero), all colors constructively interfere, resulting in white light. However, as we move away from the center, different wavelengths will interfere constructively and destructively at different points, leading to colored fringes. Therefore, **Statement 2 is True**.
**Step 3: Evaluate Statement 3**
- **Statement**: A thin transparent liquid film floating upon water, when illuminated by white light, appears colored.
- **Analysis**: When white light hits a thin film, it undergoes interference due to the varying path lengths of light reflecting off the top and bottom surfaces of the film. This interference can cause certain wavelengths to constructively or destructively interfere, leading to the appearance of colors. Thus, **Statement 3 is True**.
### Conclusion:
All three statements are true. Therefore, the correct answer is that all three statements are true.
