Question

The speed of light is 3.00 × 108 m/s in the vacuum of space. In a medium with what index of refraction would light travel slowest?
n = 1.00
n = 1.20
n = 1.50
n = 1.62

Answer 1

Index of refraction can be calculated using the following formula:

$n=\frac{c}{v}$

where $c=3 \times 10^8 \frac{m}{s}$ 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:

$v=\frac{c}{n}$

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.

$v=\frac{3 \times 10^8 \frac{m}{s}}{1.62}= 1.85185 \times 10^8 \frac{m}{s}$

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.