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(D) The fringe width $w$ in Young's double-slit experiment is given by the formula $w = \frac{\lambda D}{d}$,where $\lambda$ is the wavelength of ligh

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$w' = w$

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(D) The fringe width $w$ in Young's double-slit experiment is given by the formula $w = \frac{\lambda D}{d}$,where $\lambda$ is the wavelength of light,$D$ is the distance between the slits and the screen,and $d$ is the distance between the two slits.When a transparent sheet of thickness $t$ and refractive index $\mu$ is placed in front of one of the slits,it introduces an additional path difference of $(\mu - 1)t$. This causes a shift in the entire interference pattern.However,the fringe width $w$ depends only on the wavelength $\lambda$,the distance $D$,and the slit separation $d$. Since none of these parameters change due to the introduction of the mica sheet,the fringe width remains constant.Therefore,$w' = w$.

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