A very thin sheet of plastic (n=1.70) covers one slit of a double-slit apparatus illuminated by 630 nm light. The center point on the screen, instead of being a maximum, is dark. What is the (minimum) thickness of the plastic?
Constructive interference d*sinθ=m*λ where m=0,1,2,3,...
Destructive interference d*sinθ=(m+1/2)*λ where m=1,2,3,...
The Attempt at a Solution
Obviously this is a case of destructive interference so the sheet of plastic needs to shift the phase of that wave by λ/2. I am unsure of how to determine the thickness of the plastic necessary to make that happen though.