Double slit interference experiment is carried out with monochromatic light and interference fringes are observed. If now monochromatic light is replaced by white light, what change is expected in interference pattern?

Options

A. NO change
B. Pattern disappears
C. White and dark fringes are observed throughout
D. A few coloured fringes are observed on either side of central white fringe

Answer

To analyze the changes expected in the interference pattern when monochromatic light is replaced by white light in a double slit interference experiment, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Initial Condition**:
- In a double slit interference experiment using monochromatic light, we observe a clear pattern of alternating bright and dark fringes. The positions of these fringes are determined by the wavelength of the monochromatic light used.

2. **Effect of Replacing Monochromatic Light with White Light**:
- White light consists of multiple wavelengths (all colors of the spectrum). When white light is used, each color will produce its own interference pattern because each color has a different wavelength.

3. **Fringe Width Calculation**:
- The fringe width (β) is given by the formula:
\[ \beta = \frac{\lambda D}{d} \]
where:
- \( \lambda \) = wavelength of light,
- \( D \) = distance from the slits to the screen,
- \( d \) = distance between the slits.
- Since \( D \) and \( d \) remain constant, the fringe width will vary with the wavelength of each color in white light.

4. **Comparison of Wavelengths**:
- The wavelengths of colors in white light vary, with red light having the longest wavelength and violet light having the shortest. Thus, the fringe width for red light will be larger than that for violet light.

5. **Resulting Pattern**:
- The central maximum will appear white because all colors overlap at that point. However, as we move away from the center, different colors will produce different maxima and minima at different positions due to their varying wavelengths.
- This results in a central white fringe surrounded by colored fringes (red on the outside, violet on the inside), but the overall pattern will not be sustained as it would be with monochromatic light.

6. **Conclusion**:
- The interference pattern will consist of a central white maximum with colored fringes on either side, but it will lack the distinct and stable pattern observed with monochromatic light. Instead, there will be a gradual blending of colors, and the pattern will not be as clear or defined.

### Final Answer:
When monochromatic light is replaced by white light in a double slit interference experiment, the expected change in the interference pattern is that the central maximum will be white, surrounded by colored fringes (red on the outside and violet on the inside), but the overall pattern will be less distinct and not sustained.