In a Young's double-slit experiment the slit separation is d=0.50 mm, the screen is D=1.0 m from the slits and the wavelength in air is λ=500 nm. A…

The sheet adds an optical path $(n-1)t=0.5\times10.5\ \mu\mathrm{m}=5.25\ \mu\mathrm{m}$ to the ray from the covered slit. The central (zero path-difference) fringe must therefore move towards the covered slit, by $y=\dfrac{(n-1)tD}{d}=\dfrac{5.25\times10^{-6}\times1.0}{0.5\times10^{-3}}=10.5\ \mathrm{mm}$; (A) is correct and (D), which gives the wrong direction, is wrong. The fringe width is $\lambda D/d=1.0$ mm and is unaffected by the sheet, so (B) is wrong. At the old central point the extra path is $5.25\ \mu\mathrm{m}=10.5\lambda$, an odd multiple of $\lambda/2$, so that point is dark, not bright; (C) is wrong. Answer: A only.