Group 2030580 24 John Jairo Valencia R.

Universidad Nacional Abierta y a Distancia – UNAD UNAD Escuela de Ciencias Básicas Tecnologías e Ingenierías-ECBTI Curso: Teoria electromagnetica y Ondas Unity II

Step Step 3- Waves Waves in i n open open and enclosur enclosur e me medium diums

J ohn J ai ro Vale Valencia ncia R ojas C od: 9432 943264 6428 28

G r oup: up: 2030580_2 2030580_24 4

Tutor Tutor : Wilm Wi lme er H er nán nán Gutié Guti ér r ez

- UNAD OPEN AND DI STANCE STANCE NATI ONAL UNI UNI VE RSI TY -

Palmi Palmi r a ( V alle) lle) Ap A pri l of

Universidad Nacional Abierta y a Distancia – UNAD Escuela de Ciencias Básicas Tecnologías e Ingenierías-ECBTI Curso: Teoria electromagnetica y Ondas Unity II

1.

Explain how refraction and reflection phenomenon could be used in transmission systems.

Law of reflection: a wave that affects the separation surface between two media is reflected (partially), that is, new waves are generated that move away from said surface. The incident ray and the normal to the surface determine the plane of incidence.

Both lines form the so-called angle of incidence. The reflected ray is also contained in that plane and forms the same angle with the normal as the incident ray: Incidence angle = Reflection angle Law of refraction: when a wave hits the separation surface between two media, part of the energy is reflected and part enters the second medium. The transmitted ray is contained in the plane of incidence, but changes direction (refracted ray) forming an angle with the normal to the surface, given by Snell's Law:

 =   The reflection and refraction of waves has a great importance in communica tions. Sometimes these phenomena are favorable, as in the transmission of information through fiber optic, due to the reflection of light in this medium. On other occasions they are harmful, as in the transmission of information through copper, where we must install end-of-line resistors to minimize reflection of the signal at the end of the line, due to the change of medium. (Paz Parr, 2013, pág. 286)

2.

Explain the Snell law, the critical angle and practical applications where it could be used.

It is a formula used to calculate the angle of refraction of the light when crossing the surface of separation between two means of propagation of light (or any electromagnetic wave) with a different refractive index. The relationship between the sine of the angle of incidence and the sine of the refractive angle is equal to the ratio between the velocity of the wave in the first medium and the velocity of the wave in the second medium, or it can be understood as the product of the refractive index of the first medium by the sine of the angle of incidence is equal to the product of the refractive index of the second medium by the sine of the refractive angle, that is,: (Paz Parr, 2013, pág. 284)


 sin =  sin  refractive index of the first medium  incidence angle  refractive index of the second medium  refraction angle

The critical angle: or limit angle is also the minimum angle of incidence at which the total internal reflection occurs. The angle of incidence is measured with respect to the normal separation of the media. The critical angle is given by:

 = sin− () where  y  are the refractive indices of the media with  <  . This equation is a simple application of Snell's law where the angle o f refraction is 90 °


3.

Explain the physics behind lenses for optical diseases.

Lenses The curvature of the surface of a lens produces a refraction that varies with the angle of curvature.

Concave lenses make the image smaller Convex lenses make the image larger

The curved surface of a concave lens causes the light rays to diverge, shrinking the images


The curved surface of a concave lens causes the light rays to converge, amplifying the images (Cetto, 1987)

4.

What is the importance of the index of refraction?

The refractive index of a substance is the ratio between the speed of light in vacuum and the phase velocity of an electromagnetic signal in a specific medium. HE represented by the letter n. Because the phase velocity in any medium is less than the speed of light in vacuum, the refractive index of a substance is always an amount greater than or equal to 1 . 5.

Is it possible that a single light beam be refracted into several beans? Explain.

6.

How is it possible to use the Brewster angle in practical applications?

When a beam of light impinges with the Brewster angle, the component of the polarization parallel to the plane of incidence is canceled out in the reflected one. For this reason, the beam we see reflected has a linear polarization, just in the direction perpendicular to the plane of incidence, regardless of the type of polarization of the incident beam. It should be noted that, in the particular case of incising with a linearly polarized beam in the direction parallel to the plane of incidence, the reflected one is canceled at the Brewster angle. In this case, a total transmission of the beam between both means is produced. In general, the Brewster angle between two media depends on their electromagnetic characteristics (electrical permittivity and magnetic permeability). In the case where the


magnetic permeabilities of both media do not vary (the most frecuente), the Brewster angle can be calculated from the refractive indices of both media:

In about A.D. 150, Claudius Ptolemy gave the following measured values for the angle of incidence  and the angle of refraction  for a light beam passing from air to water:





Assuming these data are consistent with the law of refraction, use them to find the index of refraction of water. These data are interesting as perhaps the oldest recorded physical measurements.

Solution

 sin =  sin  sin =  sin      = 1     = °  = ° 1 sin10 =  sin8 


sin10 = 0.173 = 1.24  = 1sin8 0.139  = .  = °  = °′ 1 sin20 =  sin15.30  1 sin20 = 0.342 = 1.30  = sin15.30 0.263  = .  = °  = °′ 1sin30 =  sin22.30  1 sin30 = 0.5 = 1.32  = sin22.30 0.38  = .  = °  = ° 1 sin40 =  sin29   sin40 = 0.642 = 1.32  = 1sin29 0.485  = .  = °  = °


1 sin50 =  sin35  0.766 = 1.34  = 1sin50 = sin35 0.573  = .  = °  = °′ 1 sin60 =  sin40.30  0.866 = 1.34  = 1sin60 = sin40.30 0.646  = .  = °  = °′ 1 sin70 =  sin45.30  0.939 = 1.32  = 1sin70 = sin45.30 0.711  = .  = °  = °


1 sin80 =  sin50  0.984 = 1.28  = 1sin80 = sin50 0.766  = . Through the experimental exercise it can be verified that although there was no theoretical basis to describe the phenomenon, it can be verified by Snell's law, the validity of the experimental data- It is to highlight the excellent agreement between the result obtained in this experience and the tabulated value of the refractive index of water: 1.33.


Referencias Cetto, A. M. (1987). La luz en la naturaleza y en el laboratorio. Mexico: Fondo de Cultura Económica. Paz Parr, A. (2013). Electromagnetismo para Ingenieria Elecgtronica. Cali: Editorial Javeriano.

Group 2030580 24 John Jairo Valencia R.

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