Refraction and reflection

Until now we have considered waves that propagate in a single medium of indefinite extension. However, it is normal for a wave, after propagating a certain distance, to reach the surface of separation between two different media. When this occurs, two phenomena generally occur:
1) A part of the wave continues to travel through the first medium, which is known as reflection.
2) Another part propagates to the new medium, what we know as refraction.

In both cases there is usually a change of direction in relation to the incident wave.

We are going to focus on the propagation of light waves in particular, when there is a change in the speed of light, that is, of the refractive index, which we denote by n, and is given by the quotient of the speed of light in the vacuum: c, enter the speed of light in the medium in which we are v:

When the ray of light reaches the surface separating two media, a part will be reflected in the same medium from which it comes; and another part is refracted, that is, it passes to the second medium and the propagation continues producing a change in direction. Considering that the refractive index of the first medium is n1, and similarly n2 for the second medium, we call the angle of incidence to the angle that the ray makes with the normal to the surface, which in the previous image corresponds to q1; angle q’1 is called angle of reflection; while the angle q2 is called the angle of refraction. These last two angles are also measured from the normal.

The refraction and reflection of waves are governed by the following laws:
1. The incident ray, the refracted and the reflected rays are in the same plane, in which there is also normal to the surface that separates both media.
2. Law of reflection: The angle of incidence coincides with the angle of reflection: q1 = q’1
3- Snell’s Law: Thanks to this law we can calculate from the angle of incidence and the respective refractive indices n1 and n2 the refracted angle: n1 sin q1 = n2 sin q2

In the particular case in which the first medium is vacuum, and therefore n1 = 1, then Snell’s law would be as follows: sin q1 = n2 sin q2.
In the case where we could measure the angles, we could use the formula to obtain the refractive index of the second medium and therefore the speed of the second medium.

If the ray of light passes from one medium to another in which there is a lower refractive index than in the first one, that is, n1> n2; so when the angle of incidence is small there is a part that is reflected and another part that is refracted. In such a way that the previous laws stated for refraction and reflection are complied with.
For the particular case in which the incidence ray is such that the refraction ray is 90º, the angle of incidence is called the limit angle . However, in the case in which the angle of incidence is greater, no refracted ray is produced, producing an effect called total reflection .


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