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

Approximately
`2.3 * 10^(8)\; {\rm m\cdot s^(-1)}`.

Step-by-step 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 &= (c)/(v)\end{aligned}`,

Where
`c \approx 3.00 * 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 &= (c)/(n) \\ &\approx (3.00 * 10^(8))/(1.3) \; {\rm m\cdot s^(-1)} \\ &\approx 2.3 * 10^(8)\; {\rm m\cdot s^(-1)}\end{aligned}`.