A slit of width a is illuminated by red light | vedclass

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(B) Given: Wavelength $\lambda = 6500 Å = 6500 	imes 10^{-10} 	ext{ m}$,Angle $	heta = 30^{\circ}$.For the diffraction pattern of a single slit,the

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$1.3 	ext{ micron}$

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(B) Given: Wavelength $\lambda = 6500 Å = 6500 	imes 10^{-10} 	ext{ m}$,Angle $	heta = 30^{\circ}$.For the diffraction pattern of a single slit,the condition for the $n^{	ext{th}}$ minimum is given by $a \sin 	heta = n \lambda$.For the first diffraction minimum,$n = 1$.Substituting the values: $a \sin 30^{\circ} = 1 	imes (6500 	imes 10^{-10} 	ext{ m})$.Since $\sin 30^{\circ} = 0.5$,we have $a 	imes 0.5 = 6500 	imes 10^{-10} 	ext{ m}$.$a = 2 	imes 6500 	imes 10^{-10} 	ext{ m} = 13000 	imes 10^{-10} 	ext{ m}$.$a = 1.3 	imes 10^{-6} 	ext{ m} = 1.3 	ext{ micron}$.

$A$ slit of width $a$ is illuminated by red light of wavelength $6500 Å$. If the first diffraction minimum falls at $30^{\circ}$,then the value of $a$ is

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