If white light is used in a Young's double-slit experiment, the

Options

A. Bright white fringe is formed at the center of the screen
B. Fringes of different colors are observed clearly only in the first order
C. The first-order violet fringes are closer to the center of the screen than the first-order red fringes
D. The first-order red fringes are closer to the center of the screen than the first-order violet fringes

Answer

To solve the question about the effects of using white light in Young's double-slit experiment, we will analyze the behavior of different colors in the interference pattern produced.

### Step-by-Step Solution:

1. **Understanding White Light**:
White light is composed of multiple colors, each with a different wavelength. The visible spectrum includes colors such as violet, indigo, blue, green, yellow, orange, and red (VIBGYOR). The wavelengths increase from violet (shortest) to red (longest).

**Hint**: Remember that white light is a mixture of all visible colors.

2. **Central Maximum**:
In the Young's double-slit experiment, the central maximum occurs at the point where the path difference between the two waves from the slits is zero. At this point, all colors overlap and produce a bright white fringe.

**Hint**: The central maximum is where constructive interference occurs for all wavelengths.

3. **Fringe Formation**:
As we move away from the central maximum, different colors will create their own maxima and minima due to their different wavelengths. The fringe spacing (β) is given by the formula \( \beta = \frac{\lambda D}{d} \), where \( D \) is the distance from the slits to the screen, and \( d \) is the distance between the slits. Since the wavelength (λ) varies for each color, the fringe positions will differ.

**Hint**: Fringe spacing depends on the wavelength; shorter wavelengths produce closer fringes.

4. **Order of Colors**:
The first-order violet fringes will be closer to the central maximum than the first-order red fringes because violet light has a shorter wavelength compared to red light. Thus, the fringe width for violet is smaller, resulting in closer spacing.

**Hint**: Compare the wavelengths of violet and red to understand their positions on the screen.

5. **Conclusion on Options**:
- **Option 1**: Correct, as the central maximum is bright white due to overlapping colors.
- **Option 2**: Correct, as fringes of different colors can be observed, but they are more distinct in the first order.
- **Option 3**: Correct, as the first-order violet fringes are indeed closer to the center than the first-order red fringes.
- **Option 4**: Incorrect, as it contradicts the established order of colors.

### Final Answer:
Options 1, 2, and 3 are correct.