Physics
Refraction at a Plane Surface
Refraction at a plane surface refers to the bending of light as it passes from one medium to another. This phenomenon occurs due to the change in speed of light as it moves from one medium to another, causing the light rays to change direction. The amount of bending is determined by the difference in the refractive indices of the two media.
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10 Key excerpts on "Refraction at a Plane Surface"
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
When light moves from one medium into another, its direction of travel changes, and this change in direction is called refraction. The human eye is an incredible optical instrument, and, as we will see, refraction plays a major role in the way it works to produce clear vision. 26 | The Refraction of Light: Lenses and Optical Instruments 721 Design Pics/SuperStock Chapter | 26 26.1 | The Index of Refraction As Section 24.3 discusses, light travels through a vacuum at a speed of c 5 3.00 3 10 8 m/s. It can also travel through many materials, such as air, water, and glass. Atoms in the material absorb, reemit, and scatter the light, however. Therefore, light travels through the material at a speed that is less than c, the actual speed depending on the nature of the material. In general, we will see that the change in speed as a ray of light goes from one material to an- other causes the ray to deviate from its incident direction. This change in direction is called refraction. To describe the extent to which the speed of light in a material medium differs from that in a vacuum, we use a parameter called the index of refraction (or refractive index). The index of refraction is an important parameter because it appears in Snell’s law of refraction, which will be discussed in the next section. This law is the basis of all the phenomena discussed in this chapter. Definition of the Index of Refraction The index of refraction n of a material is the ratio of the speed c of light in a vacuum to the speed v of light in the material: n 5 Speed of light in a vacuum Speed of light in the material 5 c v (26.1) Table 26.1 lists the refractive indices for some common substances. The values of n are greater than unity because the speed of light in a material medium is less than it is in a vacuum. For example, the index of refraction for diamond is n 5 2.419, so the speed of light in diamond is v 5 c/n 5 (3.00 3 10 8 m/s)/2.419 5 1.24 3 10 8 m/s.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
26.2 Snell’s Law and the Refraction of Light Snell’s Law When light strikes the interface between two transparent materials, such as air and water, the light generally divides into two parts, as Figure 26.1a illustrates. Part of the light is reflected, with the angle of reflection equaling the angle of incidence. The remainder is transmitted across the interface. If the incident ray does not strike the interface at normal incidence, the transmitted ray has a different direction than the incident ray. When a ray enters the second material and changes direction, it is said to be refracted and behaves in one of the following two ways: 1. When light travels from a medium where the refractive index is smaller into a medium where it is larger, the refracted ray is bent toward the normal, as in Figure 26.1a. 2. When light travels from a medium where the refractive index is larger into a medium where it is smaller, the refracted ray is bent away from the normal, as in Figure 26.1b. These two possibilities illustrate that both the incident and refracted rays obey the principle of reversibility. Thus, the directions of the rays in part a of the drawing can be reversed to give the situation depicted in part b. In part b the reflected ray lies in the water rather than in the air. In both parts of Figure 26.1 the angles of incidence, refraction, and reflection are measured relative to the normal. Note that the index of refraction of air is labeled n 1 in part a, whereas it is n 2 in part b, because we label all variables associated with the incident (and reflected) ray with subscript 1 and all variables associated with the refracted ray with subscript 2. The angle of refraction 2 depends on the angle of incidence 1 and on the indices of refrac- tion, n 2 and n 1 , of the two media. The relation between these quantities is known as Snell’s law of refraction, after the Dutch mathematician Willebrord Snell (1591–1626), who discovered it experimentally.
eBook - PDFLet There Be Light: The Story Of Light From Atoms To Galaxies (2nd Edition)
The Story of Light from Atoms to Galaxies
- Alex Montwill, Ann Breslin(Authors)
- 2013(Publication Date)
- ICP(Publisher)
39 Chapter 3 Light as a Ray: Refraction Providing more than one quickest route When light crosses the boundary between two media, it changes direction. This phenomenon is called refraction. In this chapter we study the rules and applications of refraction . The basic rule is the same as always: it is Fermat’s principle of least time. We show that the principle leads to the experimentally established Snell’s law of refraction. Lenses are the most common example of the application of the laws of refraction . In making a lens, the trick is to make the shape such that all routes from a source A to a destination B on the other side of the lens take the same time, despite the fact that light traverses different thicknesses of glass on differ-ent routes. We spend the remainder of this section dealing with the geom-etry of the paths, and derive some simple formulae for lenses. Making visible things we cannot see We describe the effect of various combinations of lenses which make up optical systems. One fascinating example is the optical system of the human eye. We discuss some common eye defects and how these may be corrected using suitable lenses. Finally, we describe optical systems which enable us to look at things which are either too small or too far away to be seen with the naked eye. 40 Let There Be Light 2nd Edition 3.1 Refraction The refractive index As we all know, from experience of city traffic, if the speeds along different routes are not the same, the shortest route is not necessarily the quickest. We have seen already that in vacuum the speed of light is fixed at c = 2.99792458 × 10 8 m/s, equivalent to travelling a distance of approximately 7.5 times around the earth in one second . Light can also travel through certain ‘trans-parent’ materials such as air, water, glass or quartz, and there the speed is less than c .
eBook - PDF- Vanderwerf, Dennis F.(Authors)
- 2010(Publication Date)
Chapter 1 Introduction and Background 1.1 Snell’s Law of Refraction One of the most important laws in the analysis and design of prisms, and optical systems in general, is Snell’s law of refraction, named for Willebrord Snell. It relates the angles of incidence and refraction at the boundary of two materials with differing refractive index (sometimes called the index of refraction ). The refractive index n is defined as the ratio of the velocity of light in a vacuum c to the velocity of light in the material v mat : n = c v mat . (1.1) Since the velocity of light is reduced when traveling through optical materials, n is greater than unity. For the special case of air, which has a refractive index of approximately 1.0003, we assume the refractive index of air to be unity for most optical calculations. Snell’s law can be derived geometrically or from Fermat’s principle, named for Pierre de Fermat. 1 , 2 It is usually stated in the following form: n sin I = n 0 sin I 0 , (1.2) where n is the refractive index of the incident medium, and n 0 is the refractive index of the transmitting medium. I is the angle of incidence, measured relative to the boundary surface normal, and I 0 is the angle of refraction at the boundary surface of the second medium (see Fig. 1.1). Snell’s law is applicable to plane or curved surfaces, and both rays lie in a common plane called the plane of incidence . A related law for reflecting surfaces is the law of reflection. It can also be derived geometrically or by using Fermat’s principle. It is stated in the following form: I = I 0 , (1.3) where I is the angle of incidence, and I 0 is the angle of reflection, as illustrated in Fig. 1.2. Since both incident and reflected rays are in the same medium, refractive index is not a factor in the directional change, and both rays lie in the common plane of incidence. 1 2 Chapter 1 Figure 1.1 Snell’s law of refraction. Figure 1.2 Law of reflection.
eBook - PDF- Charles A. Bennett(Author)
- 2015(Publication Date)
- Wiley(Publisher)
See Section 3.7. b Far-infrared. The law of refraction, also called Snell’s law, was found experimentally by Snell early in the seventeenth century. In Figure 3.2, the light ray is incident within the incident medium and the light beam transmits into the transmitted medium. The index of refraction of the incident medium is n i and the index of refraction of the transmitted medium is n t . According to Snell’s law n i sin θ i = n t sin θ t (3.4) Finally, it is implicit in Figure 3.2 that the incident, reflected, and refracted rays all lie within a single plane. This plane is called the plane of incidence. We will refer to the case where n i < n t as external incidence. An example of external incidence occurs at an air-glass interface. Internal incidence occurs when n i > n t ; for example, when a light beam passes from glass to air. 62 REFLECTION AND REFRACTION incident ray reflected ray refracted ray incident medium transmitted medium n i n t θ i θ i θ t Figure 3.2. An interface between two media, showing the incident, reflected, and refracted rays. EXAMPLE 3.1 Show that a light beam passing through a plane slab emerges parallel to its incident direction displaced laterally by a distance d given by d = t cos θ 2 sin (θ 1 − θ 2 ) (3.5) n 1 n 1 n 2 θ 1 θ 2 θ 3 d t a γ Figure 3.3. Light rays refracting through a slab of material with parallel sides. Solution Let the slab have index of refraction n 2 and the incident and transmitted medium OVERVIEW OF REFLECTION AND REFRACTION 63 have index of refraction n 1 as shown in Figure 3.3. To show that the incident and transmitted rays are parallel, begin with Snell’s law at the first interface: sin θ 2 = n 1 n 2 sin θ 1 The beam transmitted by the first interface is incident internally on the second interface.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter- 3 Basic Concepts in Optics 1. Refractive index Refraction of light at the interface between two media The refractive index or index of refraction of a substance is a measure of the speed of light in that substance. It is expressed as a ratio of the speed of light in vacuum relative to that in the considered medium. The velocity at which light travels in vacuum is a physical constant, and the fastest speed at which energy or information can be transferred. However, light travels slower through any given material, or medium, that is not vacuum. A simplified, mathematical description of refractive index is as follows: n = velocity of light in a vacuum / velocity of light in medium Hence, the refractive index of water is 1.33, meaning that light travels 1.33 times as fast in a vacuum than it does in water. ________________________ WORLD TECHNOLOGIES ________________________ As light exits a medium, such as air, water or glass, it may also change its propagation direction in proportion to the refractive index. By measuring the angle of incidence and angle of refraction of the light beam, the refractive index n can be determined. Refractive index of materials varies with the frequency of radiated light. This results in a slightly different refractive index for each color. The cited values of refractive indexes, such as 1.33 for water, are taken for yellow light of a sodium source which has the wavelength of 589.3 nanometers. Definitions The refractive index, n , of a medium is defined as the ratio of the speed, c , of a wave phenomenon such as light or sound in a reference medium to the phase speed, v p , of the wave in the medium in question: It is most commonly used in the context of light with vacuum as a reference medium, although historically other reference media (e.g. air at a standardized pressure and temperature) have been common.
eBook - PDF- Raimo Silvennoinen, Kai-Erik Peiponen, Kari Myller(Authors)
- 2010(Publication Date)
- Elsevier Science(Publisher)
In microscopic world, the refractive index is closely related to the light Ch. 2: Light Reflection from Ideal Surface 21 field and electron interaction as it will be shown later. Substitution of Eq. 2.43 in Eq. 2.42 yields v g = c n 1 + n d n d (2.44) The formula of Eq. 2.44 has much importance in cases where information along an optical path is transferred from one place to another, such as in the case of tele-phone communication through optical fibres. In the case of measurement of the specular gloss, the dependence of the refractive index of the medium has a role because the irradiance of specularly reflected light depends on the dispersion of the medium, both for smooth and rough surfaces. We wish to emphasize once again that refractive index of medium that depends on the wavelength of the incident light, and also on the thermodynamical conditions of the medium, is a crucial intrinsic optical property that all kind of media, irrespective of their shape, texture or surface roughness, have to obey. 2.6. Normal reflection of light The simplest case of light reflection is the one where the plane wave is normally incident on planar surface. In other words, the light beam is in the direction of the normal of the plane that constitutes the interface between two media, i.e. air-transparent medium in the present case. Next, we derive a law that allows one to calculate the strength of electric field after reflection from an ideal surface. We assume that light is incident from air to a denser medium. The key points needed are results from the theory of electromagnetism, namely 22 Specular Gloss that at the interface the component of electric field that is parallel to the interface, and the component of magnetic induction that is normal to the interface are continuous functions in the interface (Born et al., 1960).
eBook - PDFPrinciples of Optics for Engineers
Diffraction and Modal Analysis
- William S. C. Chang(Author)
- 2015(Publication Date)
- Cambridge University Press(Publisher)
In a thin prism we could also consider the prism as a dielectric layer that has an n 2 layer with thickness τ embedded in a medium with index n 1 . The thickness τ varies at different position y . From Figure 1.4, we obtain τ ¼ ðy vert yÞðtan A þ tan BÞ ffi ðy vert yÞðA þ BÞ. Here, y vert is the vertex of the prism. Let there be a plane wave propagating in the z direction in a medium that has index n 1 . The beam is centered at y i . After transmitting through this composite dielectric layer, the electric field for this beam is 24 Optical plane waves in unbounded medium E out ¼ E o e jn 1 β o z e jðn 2 n 1 Þβ o τ e jωt ¼ E o e jn 1 β o z e jðn 2 n 1 Þβ o y vert e jn 1 β o sin ϕ out y e jωt ; ð1:84Þ where n 1 sin φ out ¼ ðn 2 n 1 ÞðA þ BÞ: Any plane wave that has an expðjn 1 β o sin φ out yÞ variation in y is a plane wave propagating at an angle φ out in the y–z plane. This φ out agrees with the θ out given in Eq. (1.83) above. In other words, we have just introduced an important new concept. Transmission through a thin prism could also be represented by transmission of a plane wave through a medium with a phase transmission coefficient that is a linear function of y , t ¼ t o e jðn 2 n 1 Þβ o ðy vert yÞðtan Aþtan BÞ ð1:85Þ E out ¼ tE in . Note that the results in Eqs. (1.84) and (1.85) are independent of polarization. In other words, when a plane wave is transmitted through a refractive medium with variable refractive index given in Eq. (1.85), it produces an output beam in a different direction of propagation. The conclusion is also valid for a small incidence angle θ i . Conversely, any transmission medium with a phase transmission coefficient that has a linear y variation will tilt the incident beam to a new direction of propagation like a prism. 1.3.5 Refraction in a lens A lens is probably the most commonly used optical component. It is used principally for imaging and instrumentation. Ray analysis is the principle tool used for lens design.
eBook - PDF- Y K Lim(Author)
- 1986(Publication Date)
- WSPC(Publisher)
Chapter V REFLECTION AND REFRACTION OF PLANE ELECTROMAGNETIC WAVES When an electromagnetic wave passes through the boundary between two different media, reflection and refraction occur. The consequent change of direction, phase and intensity may all be derived from the boundary conditions governing the change of the associated field vectors. 5.1 Laws of Reflection and Refraction We have seen in Sec. 2.8 that the electric field of a plane electromagnetic wave travelling parallel to the x-axis in a linear, isotropic and homogeneous medium of permittivity e and permeability u can be represented by either E (x-vt) or E (x-vt), or their vector sum, where E and E are arbitrary functions of x-vt, and v= (ue) is the phase velocity of the wave in the medium. It is often desirable to have a more general representation. Let o be the origin and k a unit vector in the direction of propagation, then -* c-for a point P in the path of the wave, OP=xk. If o' is the new + -*■ origin and we denote oo' = r , 0'P= r, then as shown in Fig. 5.1 we have Hence xfi = r + r x -vt = k • r + k • r - vt = k • r + I (k • r -
eBook - PDFColor Imaging
Fundamentals and Applications
- Erik Reinhard, Erum Arif Khan, Ahmet Oguz Akyuz, Garrett Johnson(Authors)
- 2008(Publication Date)
- A K Peters/CRC Press(Publisher)
This can be achieved by applying Snell’s law (2.102), so that sin ( Θ t ) = n 1 n 2 sin ( Θ i ) (2.125) and therefore, using Equation (B.11), we have cos ( Θ t ) = 1 − n 1 n 2 2 sin 2 ( Θ i ) (2.126) 60 2. Physics of Light By substitution into (2.123) and (2.124) expressions in n 1 , n 2 , and cos ( Θ i ) can be obtained. The reflection and transmission coefficients give the percentage of incident light that is reflected or refracted: r = E 0 , r E 0 , i (2.127a) t = E 0 , t E 0 , i (2.127b) In the case of a wave incident upon a conducting (metal) surface, light is both reflected and refracted as above, although the refracted wave is strongly attenuated by the metal. This attenuation causes the material to appear opaque. A water surface is an example of a reflecting and refracting boundary that occurs in nature. While all water reflects and refracts, on a wind-still day the Figure 2.25. On a wind-still morning, the water surface is smooth enough to reflect light specularly on the macroscopic scale; Konstanz, Bodensee, Germany, June 2005. 2.5. Reflection and Refraction 61 boundary between air and water becomes smooth on the macroscopic scale, so that the effects discussed in this section may be observed with the naked eye, as shown in Figure 2.25. 2.5.3 Reflectance and Transmittance If we assume that a beam of light is incident upon a dielectric surface at a given angle Θ i , and that the cross-section of the beam has an area A , then the incident energy per unit of time P e , i is given by P e , i = E e , i A cos ( Θ i ) , (2.128) where E e , i is the radiant flux density of Equation (2.96). Energy per unit of time is known as radiant flux and is discussed further in Section 6.2.2. Similarly, we can compute the reflected and transmitted flux ( P e , r and P e , t ) with P e , r = E e , r A cos ( Θ r ) , (2.129a) P e , t = E e , t A cos ( Θ t ) .
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