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 20^th bright fringe

3.2 mm

If shift is equivalent to n fringes then

$n=\frac{(\mu-1) t}{\lambda} \Rightarrow n \propto t \Rightarrow \frac{t_2}{t_1}=\frac{n_2}{n_1} \Rightarrow t_2=\frac{n_2}{n_1} \times t$

$t_2=\frac{20}{30} \times 4.8$ = 3.2 mm