A thin sheet of a transparent material $(μ = 1 .6)$ is placed in the path of one of the interfering beams in a YDSE using sodium light $λ = 5890 A^{0}$ .The central fringe shifts to a position originally occupied by the 12th bright fringe. Calculate the thickness of the sheet____

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$1.18 \times 10^{- 5} m$

$3.1 \times 10^{- 5} m$

$12 \times 10^{- 5} m$

$0.18 \times 10^{- 5} m$

answer is A.

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Detailed Solution

$\begin{array}{l} (μ - 1) t = nλ \\ (1 .60 - 1) t = 12 \times 5890 \times 10^{- 10} \\ t = 1 .18 \times 10^{- 5} m \end{array}$

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