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$(A)$ For diffraction at a single slit, the condition for the $n^{th}$ dark fringe is given by $d \sin 	heta = n \lambda$, where $d$ is the slit widt

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$6000$

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$(A)$ For diffraction at a single slit, the condition for the $n^{th}$ dark fringe is given by $d \sin 	heta = n \lambda$, where $d$ is the slit width, $	heta$ is the angular position, and $n$ is the order of the fringe.Given: Slit width $d = 24 	imes 10^{-5} \, cm$, angle $	heta = 30^\circ$, and order $n = 2$.Substituting the values into the formula: $24 	imes 10^{-5} 	imes \sin(30^\circ) = 2 	imes \lambda$.Since $\sin(30^\circ) = 0.5$, we have $24 	imes 10^{-5} 	imes 0.5 = 2 \lambda$.$12 	imes 10^{-5} = 2 \lambda$.$\lambda = 6 	imes 10^{-5} \, cm$.Converting to $\mathring{A}$: $1 \, cm = 10^8 \, \mathring{A}$.$\lambda = 6 	imes 10^{-5} 	imes 10^8 \, \mathring{A} = 6000 \, \mathring{A}$.

$A$ light wave is incident normally on a slit of width $24 \times 10^{-5} \, cm$. The angular position of the second dark fringe from the central maximum is $30^\circ$. What is the wavelength of light in $\mathring{A}$?

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