To get a dark spot at the centre of the pattern, you need the light coming out the two spots to have a phase difference of 180o (+/- n*360o).
Until the light hits the plastic, the light heading towards the two slits is exactly in phase. However, with in the glass the light travels slower - ie it has a shorter wavelength λplastic=λ/nplastic.
Lets say that the thickness of the plastic, L, is x*λ (x is not necessarily an integer).
If L is the minimum thickness that creates the dark spot, then L must x+1/2 of the shorter â€œin plasticâ€� wavelength
L=xλ=λ/2(n-1) = 450nm