Answer to Question #152237 in Optics for Kyra

Question

The speed of light in a vacuum is 3.00 x 108 m/s. Calculate the speed of light in diamond (n=2.42).

Answer 1

We can find the speed of light in diamond from the Snell's Law:

$$\dfrac{v_2}{v_1}=\dfrac{n_1}{n_2},$$

here, $v_1=3\cdot10^8\ \dfrac{m}{s}$ is the speed of light in the vacuum, $v_2$ is the speed of light in diamond, $n_1=1.0$ is the index of refraction of the vacuum and $n_2=2.42$ is the index of refraction of diamond.

Then, from this formula we can find the speed of light in diamond:

$$v_2=\dfrac{v_1n_1}{n_2}=\dfrac{3\cdot10^8\ \dfrac{m}{s}\cdot 1.0}{2.42}=1.24\cdot10^8 \ \dfrac{m}{s}.$$

Answer:

$v_2=1.24\cdot10^8 \ \dfrac{m}{s}.$