In a standard $YDSE$ setup,a small transparent slab of thickness $t$ and refractive index $\mu = 1.5$ is placed along the path $AS_2$ (as shown in the figure). Given that the slab thickness $t = d/4$,where $d$ is the slit separation,and the distance from the source $A$ to the slits is not explicitly needed for the shift calculation,find the position of the central maxima on the screen relative to $O$. Assume the distance between the slits and the screen is $D$.

• A
  $0.125\ D\ m$ above $O$
• B
  $0.125\ D\ m$ below $O$
• C
  $0.25\ D\ m$ below $O$
• D
  $0.25\ D\ m$ above $O$