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Lecture Notes

Module VIII The Nature and Propagation of Light

The Nature of Light

Light is an electromagnetic wave. When omitted or absorbed, italways shows particle properties. It is emitted by accelerated electriccharges that have been given excess energy by heat or electricaldischarge.Light is composed ofelementary particlescalledphotons.

The three basicdimensions of light (i.e., all electromagnetic radiation)are:

Intensity, or alternativelyamplitude, which is related to theperception ofbrightnessof the light,

Frequency, or alternativelywavelength, perceived byhumans as the colorof the light, and

Polarization (angle of vibration), which is onlyweaklyperceptible by humans under ordinary circumstances.

The speed of light in a vacuum is commonly given the symbol c. It is auniversal constant that has the value

c= 3 x 1010 cm/second

Light is electromagnetic radiation that has properties of waves. Theelectromagnetic spectrum can be divided into several bands based onthe wavelength of the light waves.

Our eyes interpret these wavelengths as different colors. If only asingle wavelength or limited range of wavelengths are present andenter our eyes, they are interpreted as a certain color. If a singlewavelength is present we say that we have monochromatic light. If

all wavelengths of visible light are present, our eyes interpret this aswhite light. If no wavelengths in the visible range are present, weinterpret this as dark.

Properties of Light: Reflection, Refraction,Dispersion, and Refractive Indices

Interaction of Light with Matter

Refraction

When light travels through something else, such as glass, diamond, orplastic, it travels at a different speed. The speed of light in a givenmaterial is related to a quantity called the index of refraction, n, which

is defined as the ratio of the speed of light in vacuum to the speed oflight in the medium:

The energy of light is related to its frequency and velocity as follows:

Where:

E = energyh = Planck's constant, 6.62517 x 10-27 erg.secn = frequency

C = velocity of light = 2.99793 x 1010

cm/secl = wavelength

The velocity of light, C, in a vacuum is 2.99793 x 1010cm/sec. Lightcannot travel faster than this, but if it travels through a substance, itsvelocity will decrease. Note that from the equation given above-

C = nl

The frequency of vibration, n, remains constant when the light passesthrough a substance. Thus, if the velocity, C, is reduced on passagethrough a substance, the wavelength, l, must also decrease.

We here define refractive index, n, of a material or substance as theratio of the speed of light in a vacuum, C, to the speed of light in amaterial through which it passes, Cm.

n = C/Cm

Note that the value of refractive index will always be greater than 1.0,since Cm can never be greater than C. In general, Cm depends on thedensity of the material, with Cm decreasing with increasing density.Thus, higher density materials will have higher refractive indices.

The change in speed that occurs when light passes from one mediumto another is responsible for the bending of light, or refraction, thattakes place at an interface. If light is traveling from medium 1 intomedium 2, and angles are measured from the normal to the interfacethe angle of transmission of the light into the second medium is relatedto the angle of incidence by Snell's law :

A light ray is a stream of light with the smallest possible crosssectional area. (Rays are theoretical constructs.) The incident ray isdefined as a ray approaching a surface. The point of incidence iswhere the incident ray strikes a surface. The normal is a constructionline drawn perpendicular to the surface at the point of incidence. Thereflected ray is the portion of the incident ray that leaves the surfaceat the point of incidence. The angle of incidence is the angle betweenthe incident ray and the normal. The angle of reflection is the anglebetween the normal and the reflected ray.

The Laws of reflection:

- The angle of incidence is equal to the angle of reflection- The incident ray, the normal, and the reflected ray are coplanar

Specular reflection (regular reflection) occurs when incident parallerays are also reflected parallel from a smooth surface. If the surface isrough (on a microscopic level), parallel incident rays are no longer

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parallel when reflected. This results in diffuse reflection (irregularreflection). The laws of reflection apply to diffuse reflection. Theirregular surface can be considered to be made up of a large numberof small planar reflecting surfaces positioned at slightly differentangles. Indirect (or diffuse) lighting produces soft shadows. It producesless eye strain than harsher, direct lighting.

Dispersion of LightThe fact that refractive indices differ for each wavelength of lightproduces an effect called dispersion. This can be seen by shining abeam of white light into a triangular prism made of glass. White lightentering such a prism will be refracted in the prism by different angles

depending on the wavelength of the light.The refractive index for longer wavelengths (red) is lower than thosefor shorter wavelengths (violet). This results in the greater angle ofrefraction for the longer wavelengths than for the shorter wavelengths.(Shown here are the paths taken for a wavelength of 800 nm, angle r800and for a wavelength of 300 nm, angle r300). When the light exits fromthe other side of the prism, we see the different wavelengths dispersedto show the different colors of the spectrum.

Polarization of Light

Normal light vibrates equally in all direction perpendicular to its path ofpropagation. If the light is constrained to vibrate in only on plane,however, we say that it is plane polarized light. The direction that thelight vibrates is called the vibration direction, which for now will beperpendicular to the direction. There are two common ways that lightcan become polarized.

There are two common ways that light can become polarized.

1. The first involves reflection off of a non-metallicsurface, such as glass or paint. An unpolarized beamof light, vibrating in all directions perpendicular to itspath strikes such a surface and is reflected. Thereflected beam will be polarized with vibrationdirections parallel to the reflecting surface(perpendicular to the page as indicated by the opencircles on the ray path). If some of this light alsoenters the material and is refracted at an angle 90o tothe path of the reflected ray, it too will becomepartially polarized, with vibration directions again

perpendicular to the path of the refracted ray, but inthe plane perpendicular to the direction of vibration inthe reflected ray (the plane of the paper, as shown inthe drawing).

2. Polarization can also be achieved by passing the lighthrough a substance that absorbs light vibrating in adirections except one. The device used to make polarizedlight in modern microscopes is a Polaroid, a trade name foa plastic film made by the Polaroid Corporation. A Polaroidconsists of long-chain organic molecules that are aligned inone direction and placed in a plastic sheet. They are placedclose enough to form a closely spaced linear grid, whichallows the passage of light vibrating only in the samedirection as the grid. Light vibrating in all other directions isabsorbed. Such a device is also called apolarizer.

Scattering

Excited electrons emit light waves, and just so happens, the oppositeis true: light waves can excite electrons. When electrons are excited bylight waves, they jump to a higher energy level. When they fall back totheir original energy level, the electrons reemit the light. This process iscalled scattering. However, when the light is reemitted by scatteringnot all of the energy is given back to the light wave; but instead, someis lost to the particle. This will result in a light wave of lower frequencyand wavelength as described by Compton's shift formula

When light is scattered on an object smaller than the wavelength olight, the process is called Rayleigh scattering. Because of the natureof Rayleigh scattering -- light waves scattered by objects smaller thanits wavelength -- it is very frequency dependent. Higher frequencyshorter wavelength, light are scattered the most while lower frequencylonger wavelength, light is scattered the least by very small particles.

The color of the sky is the direct result of Rayleigh scattering of thesunlight. Lower frequency light waves, such as red, are able to passthough a network of air particles better than higher frequency lighwaves, such as blue. During the day, the particles in the atmospherewill scatter the sunlight and lower its frequency to somewhere in theblue range. At sunset, the light waves from the sun have to travel agreater distance to reach us. Because of that, all of the light waveshave been scattered so much that it lowers the frequency to the otherend of our visible range: red.

Huygens' Principle

In many cases, light waves are very much like water waves. Onedistinct difference, however, is that water waves are waves on a 2dimensional plane (surface of the water) while light waves are waveswithin 3 dimensional space.

The wave theory, proposed by the Dutch physicist Christiaan Huygensviewed light as an impulse moving in all directions. Consider a point Pin space. If an impulse starts at P, then the effect of the impulse, aftesome time, will be equidistant from P in all directions -- one canvisualize this impulse as an expanding sphere with center P.

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Huygens called this sphere a front. Most importantly, every point on afront can be a source of new wavelets (act just like point P), and theenvelope around those wavelets forms another front. In other words, asecond front can be created from the first by making each point of thefirst front the origin of another impulse. All these impulses combine andappear as if the original front is expanding.

GeometricOptics

We define an object as anything from which light radiates.

Mirrors

Mirrors can be used to direct light and to manipulate the wavefront togive focusing and defocusing. This section looks at how images areformed using mirrors.

Graphical methods for mirrors

Principal Rays:

1. The parallel Rays drawn parallel to the axis.2. Focal ray drawn through the focal point F.3. The radial Ray drawn through or away from the center of the

curvature C.4. The central Ray drawn to the vertex.

Geometric Construction

When attempting any problem using mirrors, it is important to drawyourself a diagram showing the position of the object in relation to themirror and estimating the position of the image. This is best achievedby drawing a ray diagram. A number of different types of rays can bedrawn and these are shown in the diagram below. The image is formedwhere they intersect.

Concave

Convex

Thin Lenses

A thin lens is simply two interfaces joined together. A curved interfacetogether with a straight interface forms a plano-convex/plano-concavelens while two curved surfaces form biconvex/biconcave lenses. Thedistance between the interfaces on axis is assumed to be small in

comparison with object, image and focal distances. Vergence theoryallows a quick derivation of the propagation of light through any thislens.

Types of simple lenses

Lenses are classified by the curvature of the two optical surfaces. Alens is biconvex(ordouble convex, or just convex) if both surfaces areconvex, A lens with two concave surfaces is biconcave (or jusconcave). If one of the surfaces is flat, the lens is Plano-convex oPlano-concave depending on the curvature of the other surface. A lens

with one convex and one concave side is convex-concave omeniscus. A meniscus lens that is thinner at the centre than at theperiphery is a negative meniscus. Conversely, a meniscus lens that isthicker at the centre than at the periphery is apositive meniscus.

If the lens is biconvex or plano-convex or a positive meniscus, acollimated or parallel beam of light travelling parallel to the lens axisand passing through the lens will be converged (or focused) to a spoon the axis, at a certain distance behind the lens (known as the focalength). In this case, the lens is called apositive orconverginglens.

Ray Diagrams for Thin Lenses

Ray Diagrams

1. Parallel Ray: refracted through focus2. Focal Ray: refracted parallel3. Central Ray: passes (straight) through

Lensmaker's equation

The focal length of a lens in aircan be calculated from thelensmaker's equation:[6]

)11

)(1(1

21 RRn

f=

f is the focal length of the lens,n is therefractive indexof the lens material,R1 is the radius of curvature of the lens surface closest to thelight source,R2 is the radius of curvature of the lens surface farthest from thelight source,

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