Question

Light with a wavelength of 550 nm is traveling through a 50 kg block of ice (n=1.3). How fast is the light traveling in m/s?

Answer 1

Answer:

Approximately $2.3 \times 10^{8}\; {\rm m\cdot s^{-1}}$.

Explanation:

The refractive index of a material is inversely proportional to the speed of light in that material.

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

$\begin{aligned} n &= \frac{c}{v}\end{aligned}$,

Where $c \approx 3.00 \times 10^{8}\; {\rm m\cdot s^{-1}}$ is the speed of light in vacuum.

Rearrange this equation to find the speed of light in the given material (ice) given the refractive index of that material:

$\begin{aligned}v &= \frac{c}{n} \\ &\approx \frac{3.00 \times 10^{8}}{1.3} \; {\rm m\cdot s^{-1}} \\ &\approx 2.3 \times 10^{8}\; {\rm m\cdot s^{-1}}\end{aligned}$.