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In YDSE setup slits are illuminated by a light of wavelength 4000 $\overset{o}{A}$ and a light of unknown wavelength. It is observed that fourth dark fringe of known wavelength coincides with second bright fringe of unknown wavelength. Find the unknown (in $\overset{o}{A}$ ).

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answer is 7000.

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Detailed Solution

For $n^{t h}$ dark fringe from center, $x_{N D} = \frac{(N - 1) λ D}{2 d}$

For $N = 4, λ = 4000 \overset{o}{A} \Rightarrow x_{4 D} = \frac{7 \times 4 \times 10^{- 7} \times D}{2 d}$

For $n^{t h}$ bright fringe from center, $x_{N D} = \frac{N λ D}{d}$

For $N = 2, λ = ? \Rightarrow x_{2 B} = \frac{2 λ D}{d}$

Given that $x_{4 D} = x_{2 B}$

$\frac{7 \times 4 \times 10^{- 7} \times D}{2 d} = \frac{2 λ D}{d} \Rightarrow = 7 \times 10^{- 7} m = 7000 \overset{o}{A}$

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