Index of refraction can be calculated using the following formula:
[tex]n=\frac{c}{v}[/tex]
where [tex]c=3 \times 10^8 \frac{m}{s}[/tex] in a vacuum and "n" is the index of refraction. So we must calculate our velocity by manipulating the index of refraction formula and isolate v and so:
[tex]v=\frac{c}{n}[/tex]
We could go one by one and calculate the velocity or use logic. If you divide by a larger number the output will be a smaller number. Therefore, the answer would be n=1.62 is the slowest.
[tex]v=\frac{3 \times 10^8 \frac{m}{s}}{1.62}= 1.85185 \times 10^8 \frac{m}{s}[/tex]
By that logic when n=1 light would travel the fastest of these four scenarios. The key thing to understand about these problems is that the speed of light slows down as it goes through a medium, in a vacuum it's 3 x 10^ 8 m/s but as it goes through say air or water light slows down.
