In Young’s double slit experiment, the slits are 2mm apart and are illuminated by photons of two wavelengths $λ_{1} = 12000 A^{\circ}$ and $λ_{2} = 10, 000 A^{\circ}$ . At what minimum distance from the common central bright fringe on the screen 2m from the slit will a bright fringe from one interference pattern coincide with a bright fringe from the other ?

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8 mm

6 mm

3 mm

4 mm

answer is C.

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Detailed Solution

$\begin{array}{l} {nλ}_{1} = (n + 1) λ_{2}; n (12000) = (n + 1) (10000) \\ 6 n = (n + 1) 5; n = 5 \Rightarrow n + 1 = 6 \\ {nλ}_{1} = \frac{yd}{D}; 5 \times 12000 \times 10^{- 10} = \frac{y \times 2 \times 10^{- 3}}{2} \\ y = \frac{60 \times 10^{- 7}}{10^{- 3}}; y = 6 \times 10^{- 3}; y = 6 mm \end{array}$