White source of light is used to perform Young's double-slit experiment.

Options

A. there will not be any complete dark fringe
B. Central fringe will be white
C. Fringe adjacent to the centre will be violet
D. Fringe adjacent to the centre will be red

Explanation

To solve the problem regarding the Young's double-slit experiment using a white light source, we need to analyze the behavior of light and the resulting interference pattern. Here’s a step-by-step solution:

### Step 1: Understanding the Setup
In Young's double-slit experiment, we have two slits (Slit 1 and Slit 2) and a screen where the interference pattern is observed. The distance between the slits is denoted as 'd', and the distance from the slits to the screen is 'D'.

**Hint:** Remember that the setup consists of two coherent light sources (the slits) and a screen to observe the interference pattern.

### Step 2: White Light and Its Composition
White light is composed of multiple colors (red, orange, yellow, green, blue, indigo, violet). Each color has a different wavelength, which leads to different interference patterns.

**Hint:** Recall that white light can be dispersed into its constituent colors, which will affect the interference pattern.

### Step 3: Central Fringe
At the center of the interference pattern, all wavelengths of light (colors) arrive at the same time because they travel equal distances from both slits to the center point. This results in constructive interference, leading to a bright fringe.

**Hint:** The central fringe is where all colors overlap, resulting in a white light appearance.

### Step 4: Adjacent Fringes
As we move away from the center, different colors will interfere constructively and destructively at different points due to their varying wavelengths. The fringe adjacent to the center will be the first maximum for the shortest wavelength (violet) and the first minimum for the longest wavelength (red).

**Hint:** The fringe width is inversely proportional to the wavelength; shorter wavelengths (like violet) will create fringes closer to the center than longer wavelengths (like red).

### Step 5: Analyzing the Options
1. **There will not be any complete dark fringe:** Correct, because at any point, at least one color will be present.
2. **Center fringe will be white:** Correct, as all colors overlap at the center.
3. **Fringe adjacent to the center will be violet:** Correct, as violet has the shortest wavelength.
4. **Fringe adjacent to the center will be red:** Incorrect, as red has a longer wavelength and will be further away from the center.

**Hint:** Evaluate each option based on the principles of interference and the characteristics of light.

### Conclusion
The correct options are 1, 2, and 3. The use of white light in Young's double-slit experiment leads to a unique interference pattern where the center fringe is white, and the adjacent fringe is violet.