A screen is at a distance of 2 m from narrow slits that are illuminated with light of 589 nm. The 10th minimum lies at 0.005 m on either side of the central maximum, then the distance between the slits will be

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A screen is at a distance of 2 m from narrow slits that are illuminated with light of 589 nm. The 10th minimum lies at 0.005 m on either side of the central maximum, then the distance between the slits will be

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2.4mm

2.23mm

24mm

0.024mm

answer is B.

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Detailed Solution

$D =2 m, λ =589 nm {=589\times10}^{- 9} m, n = 10^{th} min$ , Y = 0.005m,d = ?
$\begin{array}{l} d \frac{Y}{D} = (2 n - 1) \frac{λ}{2} \\ d \frac{0 .005}{2} = (2 \times 10 - 1) \frac{589 \times 10^{- 9}}{2} \Rightarrow d = 2 .23 mm \end{array}$