$(a)\;\frac{1}{\sqrt 2} \\ (b)\;\frac{1}{\sqrt 3} \\ (c)\;3 m \\ (d)\;\frac{1}{2 \sqrt 2}\;m $

$\large\frac{d}{\lambda}=\frac{10^{-3}}{0.5 \times 10^{-6}}$$=2000$

$n= 1000$ is not << $2000$

Hence now $\Delta P= d \sin \theta $ must be used.

Hence , $d \sin \theta = n \lambda =1000 \lambda$

=> $ \sin \theta = \large\frac{1000 \lambda}{d}=\frac{1}{2}$

$\theta =30^{\circ}$

$y= D \tan \theta =\large\frac{1}{\sqrt 3}$meter

Hence b is the correct answer.

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