Answer
The difference in the traversal times is $~~0.03~\frac{L}{c}$
Work Step by Step
In general the speed of light is:
$v = \frac{c}{n},~~$ where $n$ is the index of refraction of the material
We can find the total time for pulse 1:
$T_1 = \frac{2L}{c/1.59}+\frac{L}{c/1.65}+ \frac{L}{c/1.50}$
$T_1 = \frac{3.18~L}{c}+\frac{1.65~L}{c}+\frac{1.50~L}{C}$
$T_1 = \frac{6.33~L}{c}$
We can find the total time for pulse 2:
$T_2 = \frac{L}{c/1.55}+\frac{L}{c/1.70}+ \frac{L}{c/1.60}+\frac{L}{c/1.45}$
$T_2 = \frac{1.55~L}{c}+\frac{1.70~L}{c}+\frac{1.60~L}{C}+\frac{1.45~L}{c}$
$T_2 = \frac{6.30~L}{c}$
We can find the difference in the traversal times:
$T_1-T_2 = \frac{6.33~L}{c} - \frac{6.30~L}{c}$
$T_1-T_2 = 0.03~\frac{L}{c}$
The difference in the traversal times is $~~0.03~\frac{L}{c}$
