Answer
$t = 0.40~ns$
Work Step by Step
We can write an expression for the speed of light in a medium:
$v = \frac{c}{n}$
where $n$ is the index of refraction of the medium.
We can write an expression for the time required for light to travel a distance $d$ in a medium:
$t = \frac{d}{v}$
$t = \frac{d~n}{c}$
We can find the time required for light to travel through the glass layer:
$t_g = \frac{d~n}{c}$
$t_g = \frac{(1.0\times 10^{-2}~m)(1.50)}{3.0\times 10^8~m/s}$
$t_g = 5.0\times 10^{-11}~s$
We can find the time required for light to travel through the oil layer:
$t_o = \frac{d~n}{c}$
$t_o = \frac{(5.0\times 10^{-2}~m)(1.46)}{3.0\times 10^8~m/s}$
$t_o = 2.43\times 10^{-10}~s$
We can find the time required for light to travel through the polystyrene layer:
$t_p = \frac{d~n}{c}$
$t_p = \frac{(2.0\times 10^{-2}~m)(1.59)}{3.0\times 10^8~m/s}$
$t_p = 1.06\times 10^{-10}~s$
We can find the total time:
$t = t_g+t_0+t_p$
$t = (5.0\times 10^{-11}~s)+(2.43\times 10^{-10}~s)+(1.06\times 10^{-10}~s)$
$t = 4.0\times 10^{-10}~s$
$t = 0.40~ns$
