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# In a young's double slit experiment illuminated by monochromatic light the slit separation is $0.3\;mm$ and slit- screen separation is $1.5 \;m$. If fourth bright fringe is 1 cm from central bright fringe, the wavelength of light used is

$(a)\;4000\;A^{\circ} \\ (b)\;5000\;A^{\circ} \\ (c)\;3000\;A^{\circ} \\ (d)\;1000\;A^{\circ}$

Distance of 4th bright fringe from centre
$y_4 =\large\frac{4 D \lambda}{d}$$=1\;cm$
$d= 0.3 mm$
$D= 1.5 m$
$1 \times 10^{-2}=\large\frac{4 \times 1.5 \times \lambda}{0.3 \times 10^{-3}}$
$\lambda= 0.05 \times 10^{-5}\;m$
$\quad= 5000 \times 10^{-10} \;m$
$\quad= 5000\;A^{\circ}$
Hence b is the correct answer.