Answer
$3.45\times 10^{-7}~m$
Work Step by Step
We can find the wavelength:
$\lambda = \frac{c}{f} = \frac{3.0\times 10^8~m/s}{4.00\times 10^{14}~Hz} = 7.5\times 10^{-7}~m$
We can write an equation for the electric field:
$E = E_m~sin(kx-\omega t)$
If $E = \frac{E_m}{4},$ then $sin(kx-\omega t) = \frac{1}{4}$
$(kx-\omega t) = sin^{-1}~(\frac{1}{4}) = 0.2527~rad$
If $E = 0$ at a point in the positive direction, then the angular displacement in the cycle at this point is $\pi~rad$.
We can find the distance to this point:
$(\frac{\pi~rad-0.2527~rad}{2\pi~rad})~(7.5\times 10^{-7}~m) = 3.45\times 10^{-7}~m$
