Calculate the speed of light in a medium whose refractive index is 2.4

Answer:

Approximately [tex]1.3\times 10^{8}\; \rm m\cdot s^{-1}[/tex].

Explanation:

Look up the speed of light in vacuum: [tex]c \approx 3.00\times 10^{8}\; \rm m\cdot s^{-1}[/tex]. Denote the speed as [tex]c[/tex].

If the speed of light in a medium is [tex]v[/tex], the refractive index of that medium would be:

[tex]\displaystyle n = \frac{c}{v}[/tex].

Note, that the refractive index of a medium is inversely proportional to the speed of light in this medium. A medium with a larger refractive index would thus correspond to a slower speed of light.

Rearrange this equation to find the speed of light [tex]v[/tex] in this medium:

[tex]\begin{aligned}v &= \frac{c}{n} \\ &= \frac{3.00\times 10^{8}\; \rm m\cdot s^{-1}}{2.4} \\ &\approx 1.25 \times 10^{8}\; \rm m\cdot s^{-1}\end{aligned}[/tex].

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The Book of Dragons
Chapter III The Deliverers of Their Country, an excerpt
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It all began with Effie's getting something in her eye. It hurt very much indeed, and it felt something like a red-hot spark—only it seemed to have legs as well, and wings like a fly. Effie rubbed and cried—not real crying, but the kind your eye does all by itself without your being miserable inside your mind—and then she went to her father to have the thing in her eye taken out. Effie's father was a doctor, so of course he knew how to take things out of eyes.

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