The speed of light changes when moving from one mean to another

## Refraction

The light refraction phenomenon is associated with the change of the speed of light when passing from one mean to another. The speed of light changes in the refraction, i.e., in passing from one mean to another.

For the study of refraction, the following definitions are important:

Diopter
It is the set of two media separated by a refractive surface. The substances which constitute the transparent media are called refractive means. The higher the refrangibility of a mean, the smaller will be the speed of light in this mean.
The Speed of Light in Vacuum $$(c)$$
It is $$300.000 \frac{km}{s}$$ or $$3.108 \frac{m}{s}$$ . The speed of light in air is approximated to its speed value in vacuum.
The Absolute rRefractive Index $$(n)$$
It is the ratio of the speed of light in vacuum, $$c$$ , and the speed of light in the mean in question:
$$n=\frac{velocidade\ da\ luz\ no\ v\acute{a}cuo}{velocidade\ da\ luz\ no\ meio}\ = \frac{c}{v}.$$ Examples of materials with different refractive indexes:
 Substance $$n$$ Pure water 1.33 Table salt 1.54 Diamond 2.42 Ethyl alcohol 1.36 Glycerin 1.47 Glass crown 1.52 Ice 1.31 Paraffin 1.43
The Relative Refractive Index
Its obtained from a mean $$A$$ in relation to another mean $$B$$ through the formula: $$n_{ab}=\frac{n_{A}}{n_{B}}=\frac{v_{B}}{v_{A}},$$ where $$n_A$$ is the mean's refractive index $$A$$ and $$n_B$$ is the refractive index of the mean $$B$$ .

## Refraction of Laws

For a light ray incident on two means with different refractive interface indexes, the incident ray and the refracted one, will not be in the same plane. The angles which these rays make with the normal vector of the interface between the means can be found at the law of Snell-Descartes, who says: For a monochromatic beam of light passing from one mean to another, it is constant the product of the angle's sine formed by the ray and the normal to the refractive index of the mean in which it is the radius. Mathematically, we have $$n_{1} sen(\alpha) =n_{2} sen(\beta).$$ Notice that when the light beam passes from one less refractive mean (higher speed) for a more refractive mean (slower) it approaches the normal, and vice versa. The figure below illustrates this phenomenon.

### Total Reflection

When light passes from a more refractive mean to a less refractive one, there is a limit angle, such that for angles greater than this, the light beam can not change means, so that the beam is completelly reflected at the interface between the means. This phenomenon is important for applications such as fiber optics and telescopes. The limit angle $$\Gamma$$ is defined as the incident angle which corresponds to an oblique emergency $$90^{o}$$ when light propagates from the most refractive mean for the less refractive one, ie $$sen(\Gamma)=\frac{n_{1}}{n_{2}}\text{, para }n_{1} \lt n_{2}.$$

### Diopter Plane

A diopter plane is two half homogeneous and transparent means separated by a flat surface. An observer is in the mean with refractive index $$n_1$$ , observe the ordinate $$y_1$$ of an object in a mean with refractive index $$n_2$$ as if the object was at the position whose ordinate is $$y_2$$ . See figure below. In the case of an approximately vertical observation, i.e., small angles, we can relate the position of ordinates $$y_1$$ and $$y_2$$ , with refractive indexes $$n_1$$ and $$n_2$$ , ie $$\frac{y_1}{y_2}=\frac{n_1}{n_2},$$ where $$y_2$$ is the ordinate of the position of a real object and $$y_1$$ is the ordered position where we feel that the object is.

When a light beam crosses a parallel faced blade, it leaves the mean with a given refractive index, let us say, $$n_1$$ passes through a mean with index $$n_2$$ , and returns to the refractive mean $$n_1$$. Using the laws of refraction, we find that the emerging beam in refractive mean $$n_2$$ will be parallel to the incident beam in this mean, see figure below. The distance $$d$$ in which the emerging beam deviates from the incident can be found using Snell-Descartes' law: $$d= e \frac{sen( \alpha - \beta)}{\beta},$$ where $$e$$ is the width of the blade, $$\alpha$$ is the angle of incidence and $$\beta$$ is the angle of refraction, as illustrated in FIG.
See figure above. For this system we can relate the angle between the two faces of the prism, $$\phi$$ , with the angles with internal standard $$\beta_1$$ and $$\beta_2$$ : $$\phi = \beta_1 + \beta_2.$$ It is also possible to find the angle that the incident ray in the prism will cause to the beam emerging from the material, $$\Delta$$ , ie $$\Delta = \alpha_1 + \alpha_2 - \phi,$$ where $$\alpha_1$$ and $$\alpha_2$$ are the angles that the light ray makes with the external normals of the prism.
The analysis of optical prisms reveals that the deviation assumes the minimum value, $$\Delta_{min}$$ when the angle of incidence in $$1^st$$ face and emergency on $$2^nd$$ face be equal ( $$\alpha_1 = \alpha_2$$ ) such that: $$\Delta_{min} = 2 \alpha_{1} - \phi.$$