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(C) In a double-slit experiment,the intensity at the center of the fringe pattern is zero if the path difference introduced by the plate is equal to a

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$\frac{\lambda}{2(\mu - 1)}$

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(C) In a double-slit experiment,the intensity at the center of the fringe pattern is zero if the path difference introduced by the plate is equal to an odd multiple of half-wavelength,specifically $\frac{\lambda}{2}$ for the minimum thickness.The path difference introduced by a plate of thickness $t$ and refractive index $\mu$ is given by $\Delta x = (\mu - 1)t$.For the intensity to be zero at the center,the path difference must be $\Delta x = \frac{\lambda}{2}$.Equating the two expressions: $(\mu - 1)t = \frac{\lambda}{2}$.Solving for $t$,we get $t = \frac{\lambda}{2(\mu - 1)}$.

$A$ plate of thickness $t$ made of a material of refractive index $\mu$ is placed in front of one of the slits in a double-slit experiment. What should be the minimum thickness $t$ for which the intensity at the centre of the fringe pattern is zero?

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