Answer
$L = 155~nm$
Work Step by Step
The path length difference is $2L$
To be exactly out of phase, the path length difference is $~~(\frac{\lambda}{2}+m~\lambda)$, where $m$ is some integer
We can find the smallest value of $L$:
$2L = \frac{\lambda}{2}$
$L = \frac{\lambda}{4}$
$L = \frac{620~nm}{4}$
$L = 155~nm$
