Answer to Question #162596 in Optics for Xavier

Question

State the laws of refraction and define refractive index.

Answer 1

The First Law of Refraction can be stated as follows: the angle of incidence is equal to the angle of reflection. It can be written mathematically as follows:

$$\theta_i=\theta_r.$$

The Second Law of Refraction (or Snell’s Law) can be stated as follows: the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the speed of light in the original and refracting media, or equal to the reciprocal of the ratio of the indexes of refraction. It can be written mathematically as follows:

$$\dfrac{sin\theta_i}{sin\theta_r}=\dfrac{v_i}{v_r}=\dfrac{n_r}{n_i}.$$

Therefore, the refractive index of a transparent medium is the ratio of the speed of light in vacuum, $c$, to the speed of light in the medium:

$$n=\dfrac{c}{v}.$$