In the double-slit experiment, according to Wikipedia,
the spacing of the fringes ($w$) at distance $z$ from the slits is given by $\displaystyle w = z\frac{\lambda}{d} \quad (\Leftrightarrow wd = z\lambda)$.
where $d$ is the distance between the slits and $\lambda$ is the wavelength of the light.
In a system where the distance from the slits is equal to the wavelength of the light we have $wd = \lambda^2$ or $\lambda = \pm\sqrt{wd}$.
What is the meaning of the negative wavelength?
The same argument could be said about $w=z\lambda/d$. For any positive $w$ allows solutions $z,\lambda>0$ and $z,\lambda<0$.
So if you're looking for the meaning of $\lambda<0$, you are equivalently looking for solutions $z<0$. Given that $z$ is the distance to the screen, I don't think there's any physical meaning.
That equation you are using relies on the small angle approximation $\sin\theta\approx\theta\approx\tan(\theta)=w/z,$ where $\theta$ is measured relative to the normal. Since you're setting the screen amazingly close, I doubt the resulting equation has any meaning whatsoever.
