Answer to Question #152235 in Optics for Kyra

Question

Light is travelling through air with an index of refraction of 1.00, at an angle of 30o, it then enters a mystery liquid and refracts at an angle of 14o This means that the index of refraction of the mystery liquid is:

Answer 1

We can find the index of refraction of the mystery liquid 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 mystery liquid), $\theta_i=30^{\circ}$ is the angle of incidence, $\theta_r=14^{\circ}$ is the angle of refraction.

Then, from this equation we can calculate the index of refraction of the mystery liquid:

$$n_r=\dfrac{n_isin\theta_i}{sin\theta_r}=\dfrac{1.0\cdot sin30^{\circ}}{sin14^{\circ}}=2.1$$

Answer:

$n_r=2.1$