Question

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

Answer 1

Answer:

Approximately $1.3\times 10^{8}\; \rm m\cdot s^{-1}$.

Explanation:

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

If the speed of light in a medium is $v$, the refractive index of that medium would be:

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

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 $v$ in this medium:

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