Interference fringes are observed on a screen | vedclass

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Question

(A) Given:Slit separation $d = 1 \, mm = 10^{-3} \, m$Wavelength $\lambda = 632.8 \, nm = 632.8 	imes 10^{-9} \, m$Distance $D = 100 \, cm = 1 \, m$P

Vedclass · Accepted Answer

$1.27$

Vedclass · Answer

(A) Given:Slit separation $d = 1 \, mm = 10^{-3} \, m$Wavelength $\lambda = 632.8 \, nm = 632.8 	imes 10^{-9} \, m$Distance $D = 100 \, cm = 1 \, m$Position of bright fringe $y = 1.27 \, mm = 1.27 	imes 10^{-3} \, m$The condition for a bright fringe is $y = \frac{n D \lambda}{d}$,where $n$ is the order of the fringe.Calculating $n$:$n = \frac{y d}{D \lambda} = \frac{1.27 	imes 10^{-3} 	imes 10^{-3}}{1 	imes 632.8 	imes 10^{-9}} = \frac{1.27 	imes 10^{-6}}{632.8 	imes 10^{-9}} = \frac{1270}{632.8} \approx 2$The path difference $\Delta x$ for a bright fringe is given by $\Delta x = n \lambda$.Substituting the values:$\Delta x = 2 	imes 632.8 \, nm = 1265.6 \, nm = 1.2656 \, \mu m \approx 1.27 \, \mu m$.

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