A Young's double slit experiment is conducted using white light.

In a Young's double slit experiment using white light, the central fringe is formed where the path difference $\Delta x = 0$ for all wavelengths. Since all colors interfere constructively at this point, the central fringe appears white.

For a completely dark fringe to form, destructive interference must occur simultaneously for all wavelengths at the same position. This requires the path difference to be an odd multiple of $\dfrac{\lambda}{2}$ for all wavelengths, which is impossible. Therefore, there will be no completely dark fringe.

As we move away from the central maximum, the first fringe encountered is the first minimum. The position of the first minimum for a wavelength $\lambda$ is given by $y = \dfrac{\lambda D}{2d}$. Since violet light has the shortest wavelength in the visible spectrum, its first minimum is closest to the central maximum. At this position, violet light is absent due to destructive interference, while longer wavelengths like red still have significant intensity. As a result, the fringe adjacent to the central white fringe appears red.

Answer: The central fringe will appear white.; There will be no completely dark fringe.; The fringe adjacent to the central one will be red.