A sheet of plastic (n = 1.56) covers one slit of a double slit (see the drawing). When the double slit is illuminated by monochromatic light (vacuum = 568 nm), the center of the screen appears dark rather than bright. What is the minimum thickness of the plastic?

Answer 1

all that is changed is the light is slowed in the plastic, so that there is a "distance" to be added to the plastic path (disance= deltaTimedelay*speedlight).

so at the center, the two beams are 180 deg out of phase, so it means 2*"distance" above= wavlength light.
what is time delay? well, it has to be
(n-1)thicknessplastic
2*speedlight*(n-1)thicknessplastic)=wavelength

chck my thinking.