Answer
It takes the light $~~1.42\times 10^{-13}~s~~$ to travel through layer 3.
Work Step by Step
We can find the speed in layer 3:
$v = \frac{3.0\times 10^8~m/s}{1.45} = 2.069\times 10^8~m/s$
We can use Snell's law to find the angle of refraction $\theta_4$ in layer 3:
$n_{air}~sin~\theta_1 = n_1~sin~\theta_2 = n_2~sin~\theta_2 = n_3~sin~\theta_4$
$n_{air}~sin~\theta_1 = n_3~sin~\theta_4$
$sin~\theta_4 = \frac{n_{air}~sin~\theta_1}{n_3}$
$sin~\theta_4 = \frac{1.00~sin~50^{\circ}}{1.45}$
$sin~\theta_4 = 0.5283$
$\theta_4 = sin^{-1}~(0.5283)$
$\theta_4 = 31.9^{\circ}$
We can find the distance the light travels in layer 3:
$\frac{L_3}{d} = cos~31.9^{\circ}$
$d = \frac{L_3}{cos~31.9^{\circ}}$
$d = \frac{25\times 10^{-6}~m}{cos~31.9^{\circ}}$
$d = 29.45\times 10^{-6}~m$
We can find the time it takes the light to travel through layer 3:
$t = \frac{29.45\times 10^{-6}~m}{2.069\times 10^8~m/s}$
$t = 1.42\times 10^{-13}~s$
It takes the light $~~1.42\times 10^{-13}~s~~$ to travel through layer 3.
