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  4. The first diffraction minimum due to a single slit diffraction is seen at θ=30° for a light of wavelength 5000 mathringA falling perpendicularly on the slit. The width of the slit is :-

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Q. The first diffraction minimum due to a single slit diffraction is seen at $\theta=30^{\circ}$ for a light of wavelength $5000 \,\mathring{A}$ falling perpendicularly on the slit. The width of the slit is :-

Solution:

$\sin \theta=\frac{\Delta x }{ a }=\frac{ n \lambda}{ a }$
$\sin 30^{\circ}=\frac{1 \times 5000 \times 10^{-10}}{ a }$
$a =5 \times 10^{-7} \times 2$
$a =10^{-6} m$
$a =10 \times 10^{-5} cm$