Red light of wavelength 625 , nm is incident | vedclass

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(B) The condition for principal maxima in a diffraction grating is given by $d \sin 	heta = n \lambda$, where $d = \frac{1}{N}$ is the grating elemen

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$17$

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(B) The condition for principal maxima in a diffraction grating is given by $d \sin 	heta = n \lambda$, where $d = \frac{1}{N}$ is the grating element and $N$ is the number of lines per unit length.Thus, $\frac{\sin 	heta}{N} = n \lambda$, which implies $n = \frac{\sin 	heta}{N \lambda}$.Given $\lambda = 625 \, nm = 6.25 	imes 10^{-7} \, m$ and $N = 2 	imes 10^{5} \, 	ext{lines}/m$.The maximum possible order $n$ is determined by the condition $\sin 	heta \leq 1$, so $n $n Since $n$ must be an integer, the maximum order is $n = 8$.The total number of maxima observed is given by $2n + 1$ (including the central maximum at $n=0$, and $n$ orders on both sides).Total maxima $= 2(8) + 1 = 17$.

Red light of wavelength $625 \, nm$ is incident normally on an optical diffraction grating with $2 \times 10^{5} \, \text{lines}/m$. Including the central principal maxima, how many maxima may be observed on a screen which is far from the grating?

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