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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 30th bright fringe. What should be the thickness of the sheet if the central fringe has to shift to the position occupied by 20th bright fringe

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3.8mm

1.6mm

7.6mm

3.2mm

answer is D.

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Detailed Solution

$I f s h i f t i s e q u i v a l e n t t o n f r i n g e s t h e n n = \frac{(μ - 1) t}{λ}$

$\Rightarrow n \propto t \Rightarrow \frac{t_{2}}{t_{1}} = \frac{n_{2}}{n_{1}}$

$\Rightarrow t_{2} = \frac{n_{2}}{n_{1}} \times t \Rightarrow t_{2} = \frac{20}{30} \times 4.8 = 3.2 m m$

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