In a Young’s double-slit experiment, monochromatic light of wavelength 600nm falls on two parallel slits separated by 0.50mm. The interference pattern is observed on a screen 1.0m away.
(i) Obtain an expression for the additional optical path produced when a transparent plate of thickness t and refractive index μ is introduced in front of one of the slits. Hence derive a formula for the linear shift of the entire fringe system on the screen.
(ii) A glass plate of thickness 1.0μm and refractive index 1.50 is placed as described. Calculate the number of fringes through which the central bright fringe moves and state the direction of the shift.
(iii) Find the new fringe width after the plate is inserted.