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## Homework Statement

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?

## Homework Equations

Constructive Interference:

d *sin(theta)=m*lamda

Destructive Interference:

d *sin(theta)=(m+1/2)*lamda

lamda_n=lamda/n

## 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.

Thanks!