The absolute refractive index of a medium is the ratio of the speed of light in a vacuum to the speed of light in the medium.

• The absolute refractive index of a medium is always $≥$ 1.

The following is the relationship between the absolute refractive index of a medium, the angle of incidence and the angle of refraction.

• It follows from the definition of the absolute refractive index of a medium that the absolute refractive index of air $\approx$ 1.
  • Therefore the relationship below can be simplified to the shortened — second expression (where $n_1\approx1$) in problems where light is travelling from air, to another medium — where $n$ denotes the absolute refractive index of the second medium.
• However, in problems when this is not the case, the full — first — expression can be used — where $n_1$ denotes the absolute refractive index of the first medium, and $n_2$ denotes the absolute refractive index of the second medium.

$$ \dfrac{n_2}{n_1} = \dfrac{sin\theta_1}{sin\theta_2} $$

$$ n = \dfrac{sin\theta_1}{sin\theta_2} $$

→ Faster Away Slower Towards; lower refractive index means the angle of refraction is greater and higher refractive index means the angle of refraction is smaller.

→ Usually, when light travels to be totally internally reflected in a contained object, like a circle or prism or cube, when it re-emerges into air the last reflected ray is parallel to the initial incident ray.

Snell’s Law denotes the relationship involving the angles of incidence and refraction, the wavelength of light in each medium, the speed of light in each medium.

The wave equation can be used with this to solve more complex problems.

• The bigger the refractive index $n$, the slower the light travels in that material — i.e. the smaller $v_2$ (and the smaller $\lambda_2$ ).

  → Blue Bends Best; light with smaller wavelengths and higher frequency experiences a greater refractive index in a material and thus a greater angle of refraction (causes dispersion phenomena)

$$ \dfrac{sin\theta_1}{sin\theta_2} = \dfrac{\lambda_1}{\lambda_2} = \dfrac{v_1}{v_2} = \dfrac{n_2}{n_1}  $$

$$ \dfrac{sin\theta_1}{sin\theta_2} = \dfrac{\lambda_1}{\lambda_2} = \dfrac{v_1}{v_2} $$

$$ v = f\lambda $$