The first diffraction minimum due to a single | vedclass

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(D) For a single slit diffraction,the condition for the $n^{th}$ minimum is given by $a \sin 	heta = n \lambda$. For the first minimum,$n = 1$. Given

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$10 	imes 10^{-5} \, cm$

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(D) For a single slit diffraction,the condition for the $n^{th}$ minimum is given by $a \sin 	heta = n \lambda$. For the first minimum,$n = 1$. Given: $\lambda = 5000 \, \mathring{A} = 5000 	imes 10^{-10} \, m = 5 	imes 10^{-7} \, m$ and $	heta = 30^o$. Substituting these values into the formula: $a \sin 30^o = 1 	imes (5 	imes 10^{-7} \, m)$. Since $\sin 30^o = 0.5$,we have $a 	imes 0.5 = 5 	imes 10^{-7} \, m$. $a = \frac{5 	imes 10^{-7}}{0.5} = 10 	imes 10^{-7} \, m = 10^{-6} \, m$. Converting to centimeters: $a = 10^{-6} 	imes 10^2 \, cm = 10^{-4} \, cm = 10 	imes 10^{-5} \, cm$.

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

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