A Young’s double-slit arrangement has slit separation d=0.50mm and its central point O is 1.00m away from the centre of a rectangular screen. The screen, initially perpendicular to the line joining the slits, is slowly tilted about a horizontal axis passing through its centre so that its top edge moves 2.0cm closer to the slits than its bottom edge.
With monochromatic light of wavelength λ=620nm, answer the following:
(i) Derive an expression for the path difference between the two interfering rays arriving at a point situated a distance y above O on the tilted screen.
(ii) Show that the interference fringes remain straight lines and obtain the modified expression for their spacing after the tilt.
(iii) Calculate the vertical shift of the central bright fringe on the screen due to the tilt.