Two coherent sources are placed 0.9 mm apart and the fringes are observed one metre away. The wavelength of monochromatic light used if it produces the second dark fringes at a distance of 10 mm from the central fringe will be

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$6 \times 10^{- 4} cm$

$6 \times 10^{- 7} cm$

$6 \times 10^{- 6} cm$

$1.2 \times 10^{- 4} cm$

answer is A.

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Detailed Solution

$\begin{array}{l} d = 0 .9 mm = 9 \times 10^{- 4} m; D = 1 m \\ n = 2 y = 10 \times 10^{- 3} m dsinθ = (2 n - 1) \frac{λ}{2} \\ d \frac{y}{D} = \frac{3 λ}{2}; λ = 6 \times 10^{- 6} m = 6 \times 10^{- 4} cm \end{array}$

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