In a Fraunhofer diffraction experiment, a sin | vedclass

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(D) The condition for the $n^{th}$ order minima in a single slit diffraction is given by $a \sin 	heta = n \lambda$. For small angles, $\sin 	heta \

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$1.2$

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(D) The condition for the $n^{th}$ order minima in a single slit diffraction is given by $a \sin 	heta = n \lambda$. For small angles, $\sin 	heta \approx 	heta = \frac{y}{D}$.Thus, the position of the $n^{th}$ minima is $y_n = \frac{n \lambda D}{a}$.The linear separation between the first order minima on either side of the central maxima is the width of the central maxima, which is given by $w = y_1 - (-y_1) = 2y_1 = \frac{2 \lambda D}{a}$.Given: $a = 0.5 ~mm = 0.5 	imes 10^{-3} ~m$, $\lambda = 600 ~nm = 600 	imes 10^{-9} ~m$, and $D = 50 ~cm = 0.5 ~m$.Substituting the values: $w = \frac{2 	imes 600 	imes 10^{-9} 	imes 0.5}{0.5 	imes 10^{-3}} = 1200 	imes 10^{-6} ~m = 1.2 ~mm$.

In a Fraunhofer diffraction experiment, a single slit of width $0.5 ~mm$ is illuminated by a monochromatic light of wavelength $600 ~nm$. The diffraction pattern is observed on a screen at a distance of $50 ~cm$ from the slit. What will be the linear separation of the first order minima (in $~mm$)?

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