Monochromatic light of wavelength 650nm illuminates a Young’s double-slit arrangement in which the slit separation is 0.25mm and the screen is 1.5m away. A rectangular cell 4.0mm thick, filled with a transparent liquid of refractive index 1.40, is introduced in front of one slit so that the emergent beam passes normally through the cell.
(i) Calculate the initial displacement of the central bright fringe on the screen immediately after the filled cell is placed.
(ii) The liquid is now allowed to drain out slowly until the cell becomes empty while the interference pattern is continuously observed. Determine the total number of fringes that cross the original central point on the screen during this process.
(iii) At what remaining thickness of liquid inside the cell will the central bright fringe momentarily return to its original (unshifted) position for the first time during the drainage?