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# Monochromatic light of wavelength $5000\;A^{\circ}$ is used in Y.D.S.E with slit- width $d= 1 mm$distance between screen and slits $D=1\;m$ Find the distance of 1000 th maxima

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

$\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.