When a mica sheet of thickness 7 mu m and re | vedclass

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(D) The shift in the central fringe due to the introduction of a thin sheet is given by the formula: $\Delta x = \frac{(\mu - 1) t D}{d}$.Given that t

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$6 	imes 10^{-7} \ m$

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(D) The shift in the central fringe due to the introduction of a thin sheet is given by the formula: $\Delta x = \frac{(\mu - 1) t D}{d}$.Given that the central fringe shifts to the position of the $n^{th}$ bright fringe,the shift is equal to $n \beta$,where $\beta = \frac{\lambda D}{d}$ is the fringe width.Equating the two: $\frac{(\mu - 1) t D}{d} = n \frac{\lambda D}{d}$.Simplifying,we get: $\lambda = \frac{(\mu - 1) t}{n}$.Substituting the given values: $\mu = 1.6$,$t = 7 	imes 10^{-6} \ m$,and $n = 7$.$\lambda = \frac{(1.6 - 1) 	imes 7 	imes 10^{-6}}{7} = 0.6 	imes 10^{-6} \ m = 6 	imes 10^{-7} \ m$.

When a mica sheet of thickness $7 \ \mu m$ and refractive index $\mu = 1.6$ is placed in the path of one of the interfering beams in a biprism experiment,the central fringe shifts to the position of the $7^{th}$ bright fringe. Find the wavelength of the light used.

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