Answer
$\lambda = 400~nm$
Work Step by Step
A new maximum is produced each time the mirror position $L_2$ increases by a distance of $\frac{\lambda}{2}$
We can find the wavelength:
$N = \frac{\Delta L_2}{\lambda/2}$
$N = \frac{2~\Delta L_2}{\lambda}$
$\lambda = \frac{2~\Delta L_2}{N}$
$\lambda = \frac{(2)~(100\times 10^{-6}~m)}{500}$
$\lambda = 4.0\times 10^{-7}~m$
$\lambda = 400~nm$
