In a Young’s double slit experiment performed with white light

The correct answer is Option (2) → the central fringe will be white

At the centre of the screen the path difference is zero for every wavelength, so all colours interfere constructively there and combine to give white light.

Away from the centre the fringe width \( \beta = \lambda D/d \) depends on the wavelength, so the fringes of different colours no longer coincide.

Option (1) the central fringe will be coloured — Incorrect. The central fringe is coloured only when a single colour (monochromatic light) is used; with white light every colour has its maximum there.

Option (2) the central fringe will be white — Correct. Zero path difference for all wavelengths makes the central fringe white.

Option (3) the fringe next to the white fringe will be orange — Incorrect. The first minimum is reached first for blue (the shortest wavelength), so the fringe next to the central white fringe is reddish, not orange; farther out the fringes become blue.

Option (4) All dark fringes will be completely dark fringes — Incorrect. A dark fringe for one wavelength is a bright region for another, so with white light only a few coloured fringes are seen and there are no completely dark fringes.