If the monochromatic source in Young’s double slit experiment is replaced by white light, then

The correct option is: There will be a central bright white fringe surrounded by a few coloured fringes.

Let's understand why this happens by breaking down the physics of Young's double slit experiment when using white light step-by-step:

1. Understanding White Light:
White light is not monochromatic; rather, it is a mixture of continuous wavelengths of visible light ranging from violet (approximately 400 nm) to red (approximately 700 nm).

2. The Path Difference at the Central Maxima:
At the central point on the screen (the symmetrical center between the two slits), the path difference ($\Delta x$) for light traveling from both slits is exactly zero:
$\Delta x=0$
Because the path difference is zero, constructive interference occurs at this central point for all wavelengths of light simultaneously. Since all the constituent colors of white light reconstruct constructively at the center, they recombine to form a bright, white central fringe.

3. Fringes Away from the Center:
For points away from the center, the path difference increases. The position of the $n$-th bright fringe for a wavelength $\lambda$ is given by the formula:
$y=\frac{n\lambda D}{d}$
where $D$ is the distance from the slits to the screen, and $d$ is the distance between the two slits. As we can see, the fringe position $y$ is directly proportional to the wavelength $\lambda$.

Since different colors have different wavelengths (with violet being the shortest and red being the longest), their corresponding interference maxima and minima will occur at different positions on the screen:
${\lambda }_{\text{violet}}<{\lambda }_{\text{red}}\Rightarrow y_{\text{violet}}<y_{\text{red}}$
Consequently, the fringes of different colors will not overlap perfectly anymore as we move away from the center. The region closest to the central white fringe will show colored bands, starting with violet (since it has the shortest wavelength and its first minimum/maximum occurs closest to the center) and ending with red.

4. Disappearance of the Pattern at Large Distances:
As the distance from the center increases further, the maxima of one wavelength will overlap with the minima of another. This high degree of overlap between different wavelengths results in a uniform illumination (white light) without distinct dark and bright bands, causing the interference pattern to disappear into a uniform white background after a few colored fringes.