# What is the index of refraction of a medium where the light travels in with a speed of 2.5 times 10^8 m/s?

May 20, 2017

$\text{n = 1.2}$

#### Explanation:

The index of refraction is unit less number describing how light rays will travel from one medium to the next. It is useful when applying Snell's law.

$\textcolor{w h i t e}{a a a a a a a a}$

To calculate the index of refraction, we use

$\textcolor{w h i t e}{- - - - - - -} n = \frac{c}{v}$

Where
$\text{n = index of refraction}$

$\text{c = speed of light in a vacuum} \left(3 \times {10}^{8} \frac{m}{s}\right)$

$\text{v = speed of light in the other medium} \left(\frac{m}{s}\right)$

$\textcolor{w h i t e}{- - -}$

Plug and chug

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

$n = \frac{3 \times {10}^{8} \cancel{\frac{m}{s}}}{2.5 \times {10}^{8} \cancel{\frac{m}{s}}}$

$n = 1.2$

color(blue)("Answer: n = 1.2"