Answer
$\frac{L}{\lambda} = \frac{1}{4}$
Work Step by Step
The path length difference is $2L$
Note that initially, the waves are exactly out of phase.
To be exactly in phase, the path length difference is $~~(\frac{\lambda}{2}+m~\lambda)$, where $m$ is some integer
That is, the path length difference is $~~(\frac{2m+1}{2}~\lambda)$, where $m$ is some integer
To find the smallest value of $\frac{L}{\lambda}$, we can let $m = 0$:
$2L = (\frac{2m+1}{2}~\lambda)$
$2L = \frac{\lambda}{2}$
$\frac{L}{\lambda} = \frac{1}{4}$
