In a Young's double-slit experiment,let $A$ and $B$ be the two slits. Thin films of thicknesses $t_A$ and $t_B$ and refractive indices $\mu_A$ and $\mu_B$ are placed in front of slits $A$ and $B$ respectively. If $\mu_A t_A = \mu_B t_B$,the central maximum will:

  • A
    not shift
  • B
    shift towards $A$
  • C
    shift towards $B$
  • D
    shift towards $A$ if $t_B > t_A$; shift towards $B$ if $t_B < t_A$

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When one of the slits of Young's experiment is covered with a transparent sheet of thickness $4.8 \, mm$,the central fringe shifts to a position originally occupied by the $30^{th}$ bright fringe. What should be the thickness of the sheet if the central fringe has to shift to the position occupied by the $20^{th}$ bright fringe?

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