Question

Light is traveling from air to an ‘unknown material’. The angle of incidence is measured at 30.0o​ ​, and the angle of refraction is measured at 26.3o​ ​. What is the speed of light in this ‘unknown material’.

Answer 1

Let's first find the index of refraction of the 'unknown material' from the Snell's Law:

$$n_isin\theta_i=n_rsin\theta_r,$$

here, $n_i=1.0$ is the index of refraction of the incident medium (or the air), $n_r$is the index of refraction of the refractive medium (or the 'unknown material'), $\theta_i=30^{\circ}$ is the angle of incidence, $\theta_r=26.3^{\circ}$ is the angle of refraction.

Then, from this formula we can find $n_r$:

$$n_r=\dfrac{n_isin\theta_i}{sin\theta_r}=\dfrac{sin30^{\circ}}{sin26.3^{\circ}}=1.13$$

Finally, we can find the speed of light in the ‘unknown material’ from the Snell's Law:

$$\dfrac{v_r}{v_i}=\dfrac{n_i}{n_r},$$ $$v_r=\dfrac{n_iv_i}{n_r}=\dfrac{1.0\cdot 3.0\cdot10^8\ \dfrac{m}{s}}{1.13}=2.65\cdot10^8\ \dfrac{m}{s}.$$

Answer:

$v_r=2.65\cdot10^8\ \dfrac{m}{s}.$