A single slit of width 0.1, mm is illuminated | vedclass

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(B) Given: Slit width $a = 0.1\, mm = 10^{-4}\, m$.Wavelength $\lambda = 6000\, \mathring{A} = 6000 	imes 10^{-10}\, m = 6 	imes 10^{-7}\, m$.Distan

Vedclass · Accepted Answer

$9$

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(B) Given: Slit width $a = 0.1\, mm = 10^{-4}\, m$.Wavelength $\lambda = 6000\, \mathring{A} = 6000 	imes 10^{-10}\, m = 6 	imes 10^{-7}\, m$.Distance of screen $D = 0.5\, m$.For the $n^{th}$ dark band in single slit diffraction, the condition is $a \sin 	heta = n \lambda$.For small angles, $\sin 	heta \approx 	an 	heta = \frac{x}{D}$, where $x$ is the distance from the central bright band.Thus, $a \left( \frac{x}{D} ight) = n \lambda \implies x = \frac{n \lambda D}{a}$.For the $3^{rd}$ dark band $(n = 3)$:$x = \frac{3 	imes (6 	imes 10^{-7}\, m) 	imes 0.5\, m}{10^{-4}\, m}$.$x = \frac{9 	imes 10^{-7}}{10^{-4}}\, m = 9 	imes 10^{-3}\, m = 9\, mm$.

$A$ single slit of width $0.1\, mm$ is illuminated by a parallel beam of light of wavelength $6000\, \mathring{A}$ and diffraction bands are observed on a screen $0.5\, m$ from the slit. The distance of the third dark band from the central bright band is ........ $mm$.

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