Answer
$d = 6.43~cm$
Work Step by Step
We can write an expression for the speed of light in the silicon fiber:
$v = \frac{c}{n}$
The total travel time in the silicon is $1.50~ns$
We can find the maximum distance:
$2d = v~t$
$d = \frac{c~t}{2n}$
$d = \frac{(3.0\times 10^8~m/s)(1.50\times 10^{-9}~s)}{(2)(3.50)}$
$d = 0.0643~m$
$d = 6.43~cm$
