Typical lighting effects that every person often encounters in everyday life are reflection and refraction. In this article, we consider the case when both effects manifest themselves in the framework of one process, we will focus on the phenomenon of internal full reflection.
Light reflection
Before considering the phenomenon of internal total reflection of light, one should familiarize oneself with the effects of ordinary reflection and refraction. Let's start with the first one. For simplicity, we will consider only light, although these phenomena are characteristic of a wave of any nature.
Reflection is understood to mean a change in one rectilinear trajectory along which a ray of light moves to another rectilinear trajectory when it encounters an obstacle in its path. This effect can be observed if you point the laser pointer at the mirror. The appearance of images of the sky and trees when looking at the water surface is also the result of reflection of sunlight.
The following law is valid for reflection: the angles of incidence and reflection lie in the same plane with the perpendicular to the reflecting surface and are equal to each other.
Refraction of light
The refraction effect is similar to reflection, only it arises if the obstacle in the path of the light beam is another transparent medium. In this case, part of the initial beam is reflected from the surface, and part passes into the second medium. This last part is called the refracted ray, and the angle that it forms with the perpendicular to the interface of the media is called the angle of refraction. A refracted ray lies in the same plane as reflected and incident.
Vivid examples of refraction can be called a pencil break in a glass of water or the deceptive depth of the lake when a person looks down at its bottom.
Mathematically, this phenomenon is described using Snell's law. The corresponding formula looks like this:
n 1 * sin (θ 1 ) = n 2 * sin (θ 2 ).
Here, the angles of incidence and refraction are designated as θ 1 and θ 2, respectively. The values of n 1 , n 2 reflect the speed of light in each medium. They are called the refractive indices of the media. The larger n, the slower the light moves in this material. For example, in water the speed of light is 25% less than in air, so for it the refractive index is 1.33 (for air it is 1).
The phenomenon of total internal reflection
The law of light refraction leads to one interesting result when a ray propagates from a medium with large n. Let us consider in more detail what will happen with the beam. We write out Snell's formula:
n 1 * sin (θ 1 ) = n 2 * sin (θ 2 ).
We assume that n 1 > n 2 . In this case, for the equality to remain true, θ 1 must be less than θ 2 . This conclusion is always true, since only angles from 0 o to 90 o are considered , within which the sine function is constantly increasing. Thus, upon exiting from a denser optical medium into a less dense (n 1 > n 2 ) beam, the beam deviates more from the normal.
Now we will increase the angle θ 1 . As a result, there will come a time when θ 2 will be equal to 90 o . An amazing phenomenon arises: the beam emitted from a denser medium will remain in it, that is, for it the interface between two transparent materials will become opaque.
Critical angle
The angle θ 1 , for which θ 2 = 90 o , is called critical for the considered pair of media. Any ray incident on the interface at an angle greater than critical is reflected completely in the first medium. For the critical angle θ c, we can write an expression that directly follows from Snell's formula:
sin (θ c ) = n 2 / n 1 .
If the second medium is air, then this equality is simplified to the form:
sin (θ c ) = 1 / n 1 .
For example, the critical angle for water is:
θ c = arcsin (1 / 1.33) = 48.75 o .
If you dive to the bottom of the pool and look up, you can see the sky and clouds running along it only above your own head, only the walls of the pool will be visible on the rest of the water surface.
From the above reasoning, it is clear that, in contrast to refraction, total reflection is not a reversible phenomenon, it occurs only during the transition from a denser to a less dense medium, but not vice versa.
Full reflection in nature and technology
Perhaps the most common effect in nature, which is impossible without full reflection, is the rainbow. Rainbow colors are the result of a dispersion of white light in raindrops. However, when the rays pass inside these droplets, they experience either a single or double internal reflection. That is why the rainbow always appears double.
The phenomenon of internal total reflection is used in fiber optic technology. Thanks to optical fibers, it is possible to transmit without loss electromagnetic waves over long distances.