# Thin film Interference pattern

Why exactly for this minima condition is: path difference = $$(2n-1)\lambda/2,$$ instead of $$(2n+1)\lambda/2$$?

And what is the starting order of minimal here?
Also, what does a negative path difference mean?

Let $$m=n-1$$. Then $$(2n-1) = (2m+1)$$. Therefore your two expressions are exactly the same if all integer values of $$n$$ are allowed; it is just a question of where you start the count.
If the path difference is $$x_2 - x_1$$ for two paths of lengths $$x_1,\;x_2$$ then a negative path difference means simply that $$x_1 > x_2$$. It means the first route was longer than the second, rather than shorter than the second.