Young’s double slit

1. The problem statement, all variables and given/known data
In a Young’s double-slit experiment using light of wavelength
λ, a thin piece of Plexiglas having index of refraction
n covers one of the slits. If the center point on the
screen is a dark spot instead of a bright spot, what is the
minimum thickness of the Plexiglas?

2. Relevant equations

3. The attempt at a solution
If the center is to be a dark spot then the Plexiglas must delay the light by 1/2 λ.
Call the distance from each slit to the center d.
Call the thickness of the glass t.


[itex]\frac{d}{\lambda} – (\frac{t}{\lambda/n} + \frac{d-t}{\lambda}) = \frac{1}{2}[/itex]

My reasoning is that this must be true because there is an extra wavelength in one of the paths. The book, however, reverses it. It takes what I have inside the parenthesis and subtracts that from d/λ. Other than that we agree. Why does the book reverse it?

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