A very thin sheet of plastic (n = 1.45) covers one slit of a double-slit apparatus illuminated by 570 nm light. The center point on the screen, instead of being a maximum, is dark. What is the (minimum) thickness of the plastic?
The Attempt at a Solution
So I'm a TA for a physics class and I'm a little stumped on explaining this problem. The solutions manual says that the phase shift must be an odd multiple of one half. I got that. However, it then proceeds to write down this equation:
N= t/lamda_n - t/lamda = 1/2
where t is the thickness of the plastic. Any idea how they got this relation? I would really appreciate an explanation.