Light of wavelength 5000 text{ Å} is incident | vedclass

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(C) For single slit diffraction, the condition for the $n^{th}$ minimum is given by $d \sin 	heta = n \lambda$. For small angles, $\sin 	heta \appro

Vedclass · Accepted Answer

$0.02$

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(C) For single slit diffraction, the condition for the $n^{th}$ minimum is given by $d \sin 	heta = n \lambda$. For small angles, $\sin 	heta \approx 	an 	heta = \frac{y}{D}$. For the first minimum, $n = 1$, so $d \frac{y}{D} = \lambda$. Rearranging for the slit width $d$, we get $d = \frac{\lambda D}{y}$. Given: $\lambda = 5000 	ext{ Å} = 5000 	imes 10^{-10} 	ext{ m} = 5 	imes 10^{-7} 	ext{ m}$, $D = 2 	ext{ m}$, and $y = 5 	ext{ mm} = 5 	imes 10^{-3} 	ext{ m}$. Substituting the values: $d = \frac{(5 	imes 10^{-7} 	ext{ m}) 	imes (2 	ext{ m})}{5 	imes 10^{-3} 	ext{ m}} = 2 	imes 10^{-4} 	ext{ m}$. Converting to centimeters: $d = 2 	imes 10^{-4} 	imes 10^2 	ext{ cm} = 0.02 	ext{ cm}$.

Light of wavelength $5000 \text{ Å}$ is incident normally on a slit. The first minimum of the diffraction pattern is observed to lie at a distance of $5 \text{ mm}$ from the central maximum on a screen placed at a distance of $2 \text{ m}$ from the slit. The width of the slit is: (in $\text{ cm}$)

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