Consider a bulk GaAs electro-optic device on which an electric field is applied in the $z$-direction. The field is switched between 0 and $10^5 \mathrm{~V} / \mathrm{cm}$. Calculate the length of the device needed to produce a phase change of $\pi / 2$ between the light waves polarized along $\langle 01 \overline{1}\rangle$ and $<0 \overline{1} 1\rangle$. The wavelength of the light is $1.3 \mu \mathrm{~m}$.