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In the Young's double slit experiment with sodium light, the slits are 0.589 m apart. The angular separation of the third maximum from the central maximum will be (given $λ = 589 mm)$

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$\sin^{- 1} (0.33 \times 10^{8})$

$\sin^{- 1} (0.33 \times 10^{- 6})$

$\sin^{- 1} (3 \times 10^{- 8})$

$\sin^{- 1} (3 \times 10^{- 6})$

answer is D.

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Detailed Solution

Using relation, $dsinθ = nλ \Rightarrow sinθ = \frac{nλ}{d}$

For n = 3, $sinθ = \frac{3 λ}{d} = \frac{3 \times 589 \times 10^{- 9}}{0 .589}$

$= 3 \times 10^{- 6} or θ = \sin^{- 1} (3 \times 10^{- 6})$

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