Answer
$$0.5$$
Work Step by Step
Two waves are out of phase, when the phase difference $(\phi)$ an odd multiple of $\pi$
$$\phi=(2m+1)\pi\;\;\text{for}\;m=0,1,2,3.....$$
$$\implies\frac{2\pi}{\lambda}\Delta x=(2m+1)\pi\;\;\text{for}\;m=0,1,2,3.....$$
Here, path difference is: $\Delta x=L=q\lambda$
Substituting $\Delta x=q\lambda$, we obtain
$$\frac{2\pi}{\lambda}q\lambda=(2m+1)\pi$$
$$\implies q=\frac{(2m+1)}{2}$$
For the smallest value of $q$ that put $A$ and $B$ exactly out of phase with each other after the reflections, we put $m=0$
Therefore,
$$q=\frac{(2\times0+1)}{2}=0.5$$
