In a Young's double-slit experiment the slit separation is 1.0 mm, the screen is 1.0 m away and the wavelength is 600 nm. A thin transparent slab of…

The slab adds an extra optical path $(\mu-1)t=0.5\times15\ \mu\mathrm{m}=7.5\ \mu\mathrm{m}$ on its own path, so the point of zero net path difference moves toward the covered slit: (A) is true. The shift is $\dfrac{(\mu-1)tD}{d}=\dfrac{7.5\times10^{-6}\times1}{10^{-3}}=7.5\ \mathrm{mm}$, so (B) is true. At the old central point the path difference is $7.5\ \mu\mathrm{m}/600\ \mathrm{nm}=12.5$ wavelengths, a half-integral number, giving destructive interference and zero intensity, so (C) is false. The fringe width $\beta=\lambda D/d=0.6\ \mathrm{mm}$ depends only on $\lambda$, $D$ and $d$ and is unchanged, so (D) is false.