Two slits separated by a distance of 1, mm ar | vedclass

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Question

(A) Given: Slit separation $d = 1\, mm = 10^{-3}\, m$,wavelength $\lambda = 6.5 	imes 10^{-7}\, m$,distance to screen $D = 1\, m$.The fringe width is

Vedclass · Accepted Answer

$1.625\, mm$

Vedclass · Answer

(A) Given: Slit separation $d = 1\, mm = 10^{-3}\, m$,wavelength $\lambda = 6.5 	imes 10^{-7}\, m$,distance to screen $D = 1\, m$.The fringe width is given by $\beta = \frac{\lambda D}{d} = \frac{6.5 	imes 10^{-7} 	imes 1}{10^{-3}} = 6.5 	imes 10^{-4}\, m = 0.65\, mm$.The position of the $n^{	ext{th}}$ bright fringe is $y_{n, 	ext{bright}} = n\beta$.For the $5^{	ext{th}}$ bright fringe,$y_{5, 	ext{bright}} = 5\beta$.The position of the $n^{	ext{th}}$ dark fringe is $y_{n, 	ext{dark}} = (n - 0.5)\beta$.For the $3^{	ext{rd}}$ dark fringe,$y_{3, 	ext{dark}} = (3 - 0.5)\beta = 2.5\beta$.The distance between the $5^{	ext{th}}$ bright fringe and the $3^{	ext{rd}}$ dark fringe is $\Delta y = y_{5, 	ext{bright}} - y_{3, 	ext{dark}} = 5\beta - 2.5\beta = 2.5\beta$.Substituting the value of $\beta$: $\Delta y = 2.5 	imes 0.65\, mm = 1.625\, mm$.

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