Answer
To S', the time interval between flashes is $~~4.39\times 10^{-6}~s$
Work Step by Step
We can find $\gamma$:
$\gamma = \frac{1}{\sqrt{1-\beta^2}}$
$\gamma = \frac{1}{\sqrt{1-0.480^2}}$
$\gamma = 1.14$
We can find the temporal coordinate $t_1'$ of the big flash:
$t_1' = \gamma~(t_1-vx_1/c^2)$
$t_1' = 1.14~[(0)-\frac{-(0.480)(1200~m)}{(3.0\times 10^8~m/s)}]$
$t_1' = (1.14)(1.92\times 10^{-6}~s)$
$t_1' = 2.189\times 10^{-6}~s$
We can find the temporal coordinate $t_2'$ of the small flash:
$t_2' = \gamma~(t_2-vx_2/c^2)$
$t_2' = 1.14~[(5.00\times 10^{-6}~s)-\frac{-(0.480)(480~m)}{(3.0\times 10^8~m/s)}]$
$t_2' = (1.14)(5.00\times 10^{-6}~s+0.768\times 10^{-6}~s)$
$t_2' = 6.576\times 10^{-6}~s$
We can find $\Delta t'$:
$\Delta t' = t_2'-t_1'$
$\Delta t' = 6.576\times 10^{-6}~s-2.189\times 10^{-6}~s$
$\Delta t' = 4.39\times 10^{-6}~s$
To S', the time interval between flashes is $~~4.39\times 10^{-6}~s$
