Q. 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
A) $3.8\ mm$
B) $1.6\ mm$
C) $7.6\ mm$
D) $3.2\ mm$
Explanation
(d) If shift is equivalent to $n$ fringes then
$n = \frac{(\mu - 1)t}{\lambda} \Rightarrow n \propto t \Rightarrow \frac{t_{2}}{t_{1}} = \frac{n_{2}}{n_{1}} \Rightarrow t_{2} = \frac{n_{2}}{n_{1}} \times t$
$t_{2} = \frac{20}{30} \times 4.8 = 3.2mm$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.