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Notes On Light - 2

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Published in: Physics
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Physics

Aritra D / Kolkata

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  1. Light Part — 2 In the last lesson on Light, we were introduce to what Light is and its different characteristics. In the previous lesson, we were introduced to the concepts of Reflection, Refraction and Total Internal Reflection. We also traced the light rays in Plane mirrors and curved mirrors — Concave and Convex. In this lesson, we will continue to study about light and explore the different phenomena by trying to understand the reasons behind them. Reflection of light may be specular or diffuse. The first occurs on a blank mirroring surface that retains the geometry of the beams of light. The second occurs on a rougher surface, not retaining the imaging geometry, only the energy. Diffuse Reflection When light strikes a rough or granular surface, it bounces off in all directions due to the microscopic irregularities of the interface, as illustrated in the figure given below. Thus, an image is not formed. This is called diffuse reflection. The exact form of the reflection depends on the structure of the surface. 3 Diffuse reflection from a rough surface Perfect Mirrors A perfect mirror is a theoretical mirror that reflects light (and electromagnetic radiation in general) perfectly, and does not transmit it. Domestic mirrors are not perfect mirrors as they absorb a significant portion of the light, which falls on them. Dielectric mirrors are glass or other substrates on which one or more layers of dielectric material are deposited, to form an optical coating. A very complex dielectric mirror can reflect up to 99.999% of the light incident upon it, for a narrow range of wavelengths and angles. A simpler mirror may reflect 99.9% of the light, but may cover a broader range of wavelengths. Retro Reflection Retro reflectors are used both in a purely specular and in a diffused mode. A simple retro reflector can be made by placing two ordinary mirrors mutually perpendicular to one another. The image produced is the inverse of one produced by a single mirror.
  2. Applications also include simple radar reflectors for ships, and the Lunar Laser Range program based on four retro reflectors placed at the Apollo 11, 14, and 15 sites and the Lunakhod 2 rover. In such applications, it is imperative that the corner angle is exactly 900. A deviation by an angle 5 will cause the returned beam to deviate by 25 from the incoming beam. Surfaces may also be retroref/ective. The structure of these surfaces is such that light is returned in the direction from which it came. A surface can be made partially retroref/ective by depositing a layer of tiny refractive spheres on it or by creating small pyramid like structures (cube corner reflection). In both cases, internal reflection causes the light to be reflected back to where it originated. This is used to make traffic signs and automobile license plates reflect light mostly back in the direction from which it came. In this application, a perfect retroreflection is not desired, since the light would then be directed back into the headlights of an oncoming car rather than to the driver's eyes. The description of retro reflectors may illustrate an important property of all images formed by reflecting or refracting surfaces: An image formed by one surface can serve as the object for a second imaging surface. The principle of a retro reflector Optical aberrations caused by curved mirrors Spherical aberration: A simple mirror with a spherical surface suffers from the optical imperfection called spherical aberration: Light striking nearer the periphery focuses closer to the mirror, while light striking near the centre focuses farther away. While spherical mirrors are the most convenient to grind and polish, spherical aberration can be eliminated by grinding and polishing the surface to a paraboloid of revolution. Then parallel rays striking all parts of the mirror are reflected to the same focus. Comma: The principal disadvantage of a parabolic mirror is that it produces good images over only a relatively small field of view, that is, for light that strikes the mirror very nearly parallel to the optical axis. In a photograph of a field of stars, the star images near the centre of the picture will appear as sharp, round dots, whereas those near the corners, which are formed
  3. by light coming in at an angle to the optical axis, are distorted into tiny "tear drops" or "commas" pointing towards the centre of the photograph. The shape of these images accounts for the name "coma" given to this type of aberration that distorts images formed by light that strikes the mirror off-axis. Astigmatism: Astigmatism occurs when rays of light in different planes do not focus at the same distance from the mirror. Such aberrations may be caused by mechanical distortions of large mirrors. Curvature of field: This is an aberration in which the image is sharp, but different parts of it are formed at different distances from the mirror, so that a flat detector cannot capture the whole image. Distortion: This is an aberration in which the image may be sharp, but its shape is distorted, e.g., if straight lines in the object plane are imaged as curved lines. Distortion may vary within the field of view, being most noticeable near the edges of the field of view. Vignetting: This is an aberration that causes a darkening of the image towards the corners of the field of view. Reflecting Telescopes A telescope is an instrument designed for the observation of remote objects. There are three main types of optical astronomical telescopes: • The refracting (dioptric) telescope, which uses an arrangement of lenses; • The reflecting (catoptric) telescope, which uses an arrangement of mirrors; and • The catadioptric telescope, which uses a combination of mirrors and lenses. The Italian monk Niccolo Zucchi is credited with making the first reflector in 1616, but he was unable to shape the concave mirror accurately and he lacked of means of viewing the image without blocking the mirror, so he gave up the idea. The first practical reflector design is due to James Gregory. In Optica Promota (1663), he described a reflector using two concave mirrors. A working example was not built until 10 years later by Robert Hooke. Sir Isaac Newton is often credited with constructing the first "practical" reflecting telescope after his own design in 1668. However, because of the difficulty of precisely producing the reflecting surface and maintaining a high and even reflectivity, the reflecting telescope did not become an important astronomical tool until a century later. Telescopes increase the apparent angular size of distant objects, as well as their apparent brightness. If the telescope is used for direct viewing by the human eye, an eyepiece is used to view the image. And most, if not all, eyepiece designs use an arrangement of lenses. However, in most professional applications the image is not viewed by the human eye, but is captured by photographic film or digital sensors, without the use of an eyepiece. In this configuration, telescopes are used as pure reflectors. Optical Prisms
  4. Optical prisms are often associated with dispersion of a white light beam into a spectrum. However, the most common use of optical prisms is in fact to reflect light without dispersing it, in order to alter the direction of a beam, shift it by a certain amount in a given direction, and eventually rotate and / or flip the image at the same time. Reflective Prisms Reflective prisms utilize the internal reflection at the surfaces. In order to avoid dispersion, light must enter and exit the prism orthogonal to a prism surface. If light inside the prism hits one of the surfaces at a sufficiently steep angle, there is total internal reflection, and all of the light is reflected in accordance with the law of reflection (angle of incidence = angle of reflection). This makes a prism a very useful substitute for a planar mirror in some situations. Thus, reflective prisms may be used to alter the direction of light beams, to offset the beam, and to rotate or flip images. Single Right-Angled Triangular Prism The right-angle triangular prism is the simplest type of optical prism. It has two right-angled triangular and three rectangular faces. As a reflective prism, it has two modes of operations: 1. The light beam enters orthogonal to one of the small rectangular faces, is reflected by the large rectangular face, and exits orthogonal to the other small rectangular face. The direction of the beam is altered by 900, and the image is reflected left-to-right, as in an ordinary plane mirror. 2. The light beam enters orthogonal to the large rectangular face, is reflected twice by the small rectangular faces, and exits again orthogonal to the large rectangular face. The beam exits in the opposite direction and is offset from the entering beam. The image is rotated 1800, and by two reflections, the left-to-right relation is not changed. In both modes, there is no dispersion of the beam, because of normal incidence and exit. As the critical angle is approximately 410 for glass in air, we are also guaranteed that there will be total internal reflection, since the angles of incidence is always 410. Truncated Right-Angled Prism
  5. A truncated right angle (Dove) prism may be used to invert an image. A beam of light entering one of the sloped faces of the prism at an angle of incidence of 450, undergoes total internal reflection from the inside of the longest (bottom) face, and emerges from the opposite sloped face. Images passing through the prism are flipped, and because only one reflection takes place, the image's handedness is changed to the opposite sense. Dove prisms have an interesting property that when they are rotated along their longitudinal axis, the transmitted image rotates at twice the rate of the prism. This property means they can rotate a beam of light by an arbitrary angle, making them useful in beam rotators, which have applications in fields such as interferometry, astronomy, and pattern recognition. Pentaprism In a pentaprism, the light beam enters orthogonal to one of the two orthogonal rectangular faces, is reflected by the two neighbouring faces, and exits orthogonal to the face that is orthogonal to the entry face. Thus, the direction of the beam is altered by 900, and as the beam is reflected twice, the prism allows the transmission of an image through a right angle without inverting it. During the reflections inside the prism, the angles of incidence are less than the critical angle, so there is no total internal reflection. Therefore, the two faces have to be coated to obtain mirror surfaces. The two orthogonal transmitting faces are often coated with an antireflection coating to reduce reflections.
  6. The fifth face of the prism is not used, but truncates what would otherwise be a sharp angle of 250 joining the two mirror faces. This fifth face is usually smaller than the two mirror faces, in order to let the mirror faces receive all beams entering the input face. Roofed Pentaprism A roofed pentaprism is a combination of an ordinary pentaprism and a right-angle triangular prism. The triangular prism substitutes one of the mirror faces of the ordinary pentaprism. Thus, the handedness of the image is changed. This construction is commonly used in the viewfinder of single-lens reflex cameras. Dispersive Prisms A light beam striking a face of a prism at an angle is partly reflected and partly refracted. The amount of light reflected is given by Fresnel's equations, and the direction of the reflected beam is given by the law of reflection (angle of incidence = angle of reflection). The refracted light changes speed as it moves from one medium to another. This speed change causes light striking the boundary between two media at an angle to proceed into the new medium at a different angle, depending on the angle of incidence, and on the ratio between the refractive indices of the two media (Snell's law). Since the refractive index varies with wavelength, light of different colours is refracted differently. Blue light is slowed down more than red light and will therefore be bent more than red light. Optical aberrations caused by lenses Chromatic Aberration in Lenses: A convex lens may be taken as equivalent to two small- angled prisms placed base to base and the concave lens as equivalent to such prisms placed vertex to vertex. Thus, a polychromatic beam incident on a lens will get dispersed. The parallel beam will be focused at different coloured focii. This defect of the image formed by spherical lenses is called chromatic aberration. It occurs due to the dispersion of a polychromatic incident beam.
  7. F Chromatic aberration Dispersion of light through a Prism Newton used a prism to demonstrate dispersion of light. White light from a slit falls on the face AB of the prism and light emerging from face AC is seen to split into different colours. Coloured patches can be seen on a screen. The face AC increases the separation between the rays refracted at the face AB. The incident white light PQ thus splits up into its component seven colours: Violet, indigo, blue, green, yellow, orange and red (VIBGYOR). The wavelengths travelling with different speeds are refracted through different angles and are thus separated. This splitting of white light into component colours is known as dispersion. MR and MV correspond to the red and violet light respectively. These colours on the screen produce the spectrum. The bending of the original beam PQN along MR and MV etc. is known as deviation. The angle between the emergent ray and the incident ray is known as the angle of deviation. Thus, 5v and 5r tea-ra I,' R Passage of light through a glass slab Rainbow formation Dispersion of light by a prism Dispersion of sunlight through suspended water drops in air produces a spectacular effect in nature in the form of rainbow on a rainy day. With Sun at our back, we can see a brighter and another fainter rainbow. The brighter one is called the primary rainbow and the other one is said to be secondary rainbow. Sometimes we see only one rainbow. The bows are in the form of coloured arcs whose common centre lies at the line joining the Sun and our eye. Rainbow
  8. can also be seen in a fountain of water in the evening or morning when the sunrays are incident on the water drops at a definite angle. Primary Rainbow: The primary rainbow is formed by two refractions and a single internal reflection of sunlight in a water drop. Descartes explained that rainbow is seen through the rays, which have suffered minimum deviation. Parallel rays from the Sun suffering deviation of 1370.29' or making an angle of 420.31' at the eye with the incident ray, after emerging from the water drop, produce bright shining colours in the bow. Dispersion by water causes different colours (red to violet) to make their own arcs which lie within a cone of 430 for red and 410 for violet rays on the outer and inner sides of the bow. I.SLR geerdxc•p O "t- light. S unhght cf incident (a) A ray suffering two refractions and one internal reflection in a drop of water. Mean angle of minimum deviation is 137229' and (b) dispersion by a water drop. Secondary Rainbow: The secondary rainbow is formed by two refractions and two internal reflections of light on the water drop. The angles of minimum deviations for red and violet colours are 2310 and 2340. Respectively, so they subtend a cone of 510 for the red and 540 for the violet colour. From the figure, it is clear that the red colour will be on the inner and the violet colour on the outer side of the bow. 44 Formation of the secondary rainbow Colourful optical phenomena that are not rainbows: Halos are a class of phenomena caused by ice crystals in the atmosphere. The most common is the 222 radius bright halo around the sun (or the moon) caused by thin high cirrostratus clouds. The sharp inner edge may be red. The sky inside the halo is darker.
  9. Parhelia are among the most frequent halo phenomena, caused by planar crystals lying mostly horizontal in the atmosphere. Thus, when the sun is low, light passes through the crystal side faces inclined 602 to each other, and we see bright halos on both sides of the sun, about 222 off. These "sundogs" are often brightly coloured because of differential refraction in the ice crystals. Pillars are narrow columns of light apparently beaming directly up and sometimes downwards from the sun, most frequently seen near to sunset or sunrise. They can be 5 — 100 tall and occasionally even higher. Pillars are not actually vertical rays; they are instead the collective glints of millions of ice crystals. As they take on the colours of the sun and clouds, they can appear white and at other times shades of yellow, red or purple. The circumzenithal arc is also a beautiful halo phenomenon, like an upside down rainbow. Coronae are halo-like, but smaller coloured rings around the sun or moon, which are produced by scattering in water droplets rather than ice crystals. The glory phenomenon is a colourful set of rings scattered from cloud or fog droplets. The rings are centred on the shadow of your head. Fogbows are also a scattering phenomenon. They are almost as large as rainbows, and much broader. Heiligenschein is caused by the focusing of dewdrops, and backscattering of the focused light through the drops. Iridescence in clouds most often occurs close to the sun, but is best seen if the sun is hidden. It is caused by diffraction in small same-size droplets in thin tropospheric clouds. Nacreous or mother-of-pearl clouds are a much rarer manifestation of iridescence. They can glow very brightly and are far higher than ordinary tropospheric clouds. Diffraction Light can also bend around corners. When light from a point source falls on a straight edge and casts a shadow, the edge of the shadow is not a perfectly sharp step edge. Neither is the shadow of the edge just smeared out. There is some light in the area that we expected to be in the shadow, and we find alternating bright and dark fringes in the illuminated area close to the edge. This is the result of interference between many light waves (Huygens' Principle). Such effects are referred to as diffraction. We shall now describe the intensity patterns that are observed when light waves pass through a single slit, through two parallel slits, and through multiple parallel slits. We shall also describe the pattern observed as a result of light passing through a circular and an annular aperture. It is customary to distinguish between two descriptions of diffraction: • Fresnel (near-field) diffraction occurs when both the light source and the observation plane are close to the aperture. Since the wave fronts arriving at the aperture and observation plane
  10. are not planar, the curvature of the wave fronts must be taken into account. We will discuss Fresnel diffraction at a later stage. • Fraunhofer (far-field) diffraction is observed when the wave fronts arriving at the aperture and the observation plane may be considered planar. This is usually taken to imply that both the light source and the observation plane must be sufficiently far away from the slit to allow all light rays to be parallel. However, a thin lens having the light source in its primary focal point will collimate the beam before it reaches the aperture; and similarly a lens behind the aperture may collimate the light beam traveling towards the observation plane. The nearfield/farfield limit is the same as the hyperfocal distance. The Diffraction Grating A diffraction grating is an assembly of narrow slits or grooves, which by diffracting light produces a large number of beams, which can interfere in such a way as to produce spectra. Since the angles at which constructive interference are produced by a grating depend on the wavelengths of the light being diffracted, the various wavelengths in a beam of light striking the grating will be separated into a number of spectra, produced in various orders of interference on either side of an undeviated central image. A simple Spectroheliograph A spectroheliograph produces monochromatic images of the Sun. In the simplest form of the instrument, an image of the Sun from a solar telescope is focused on a plane where a narrow slit lets light into a spectrograph. At the rear end of the spectrograph, a slightly tilted concave collimating mirror reflects the light coming from the slit back onto a plane reflecting diffraction grating. Part of the dispersed light from the grating is focused by a second concave mirror, identical to the first mirror, onto an exit slit identical to the entrance slit. By symmetry of the optical system, the portion of the solar disk imaged on the entrance slit is reimaged in the plane of the exit slit with the same image scale but in dispersed wavelength. The light imaged along the exit slit then corresponds to the portion of the solar image falling on the entrance slit, but in the light of only a narrow region of the spectrum, as determined by the spectrographic dispersion. Therefore, the spectral dispersion and the width of the exit slit determine how "monochromatic" the output will be. The dispersion is determined by the grating characteristics and the spectral order, while the particular wavelength sampled is set by the grating angle. By letting the image of the Sun move in a uniform transverse motion the entrance slit is scanned across the solar image. By moving a photographic film behind the exit slit at the same speed as the image is moving across the entrance slit — or performing a corresponding sequential readout of a linear array of digital sensors behind the slit — a monochromatic image of the Sun is recorded. Such images are routinely made — both ground-based and from satellites — in order to study the solar magnetic field as well as active regions, flares and solar eruptions etc. Scattering
  11. Scattering is a physical process that causes radiation to deviate from a straight trajectory. We saw this in the introductory sections on reflection: If there were microscopic irregularities in the surface, we would get diffuse instead of specular reflection. The same goes for radiation passing through a transparent medium: If there are non-uniformities like particles, bubbles, droplets, density fluctuations etc., some of the radiation will deviate from its original trajectory. In a physical description of the phenomenon, we distinguish between two types of scattering, namely elastic and inelastic. Elastic scattering involves no (or a very small) loss or gain of energy by the radiation, whereas inelastic scattering does involve some change in the energy of the radiation. If the radiation is substantially or completely extinguished by the interaction (losing a significant proportion of its energy), the process is known as absorption. When radiation is only scattered by one localized scattering centre, this is called single scattering. Single scattering can usually be treated as a random phenomenon, often described by some probability distribution. Often, many scattering centres are present, and the radiation may scatter several times, which is known as multiple scattering. With multiple scattering, the randomness of the interaction tends to be averaged out by the large number of scattering events, so that the final path of the radiation appears to be a deterministic angular distribution of intensity as the radiation is spread out. Using an imaging device, we will not get a sharp, diffraction limited image of the object, but a more blurred image that is the result of a convolution of the image with a point-spread function that includes both diffraction and scattering. Since the intensity distribution of the object is often unknown, a difficult challenge is the "inverse scattering problem", in which the goal is to observe scattered radiation and use that observation to determine either the scattering parameters or the distribution of radiation before scattering. In general, the inverse is not unique, unless the scattering profile can be found by observing the image of some well-known object through the same scattering medium. Light scattering and absorption are the two major physical processes that contribute to the visible appearance of physical objects. The spectral distribution of absorption determines the colour of a surface, while the amount of scattering determines whether the surface is mirror- like or not. The size of a scattering particle is defined by the ratio of its characteristic dimension and the wavelength of the scattered light: 2 Ttr 1 The wavelength dependence of scattering is primarily determined by this ratio of the size of the scattering particles to the wavelength of the light: • Scatter diameters much less than the wavelength results in Rayleigh scattering. • Larger diameters result in Mie scattering.
  12. Rayleigh scattering occurs when light travels in transparent solids and liquids, but is most prominently seen in gases. The amount of Rayleigh scattering that occurs to a beam of light is dependent upon the size of the particles and the wavelength of the light; in particular, the scattering coefficient, and hence the intensity of the scattered light, varies for small size particles inversely with the fourth power of the wavelength. This wavelength dependence (æÄ-4) means that blue light is scattered much more than red light. In the atmosphere, the result is that blue light is scattered much more than light at longer wavelengths, and so one sees blue light coming from all directions of the sky. At higher altitudes, high up in the mountain or in an airplane, we can observe that the sky is much darker because the amount of scattering particles is much lower. When the Sun is low on the horizon the sunlight must pass through a much greater air mass to reach an observer on the ground. This causes much more scattering of blue light, but relatively little scattering of red light, and results in a pronounced red-hued sky in the direction towards the sun. Surfaces described as white owe their appearance almost completely to the scattering of light by the surface of the object. Absence of surface scattering leads to a shiny or glossy appearance. Light scattering can also give colour to some objects, usually shades of blue (as with the sky, the human iris, and the feathers of some birds). Scattering by spheres larger than the Rayleigh range is usually known as Mie scattering. In the Mie regime, the shape of the scattering centre becomes much more significant and the theory only applies well to spheres and, with some modification, spheroids and ellipsoids. Closed-form solutions for scattering by certain other simple shapes exist, but no general closed-form solution is known for arbitrary shapes. The wavelength dependence of Mie scattering is approximately described by I/N. Both Mie and Rayleigh scattering are considered elastic scattering processes, in which the energy (and thus wavelength and frequency) of the light is not substantially changed. However, electromagnetic radiation scattered by moving scattering centres does undergo a Doppler shift, which can be detected and used to measure the velocity of the scattering centres in forms of techniques such as LIDAR and radar. This shift involves a slight change in energy. At values of the ratio of particle diameter to wavelength more than about 10, the laws of geometric optics are mostly sufficient to describe the interaction of light with the particle, and at this point, the interaction is not usually described as scattering. Some effects of scattering If we perform passive imaging of a simple object that is illuminated by, e.g., sunlight, a detector element in the focal plane of the imaging system will in general receive part of the radiation that is reflected off a specific part of the surface of the object. The incident radiation will consist of several components: 1. Specular reflection, governed by the law of reflection.
  13. 2. Diffuse reflection, governed by Lambertian reflection. 3. In addition, the detector element will receive some diffuse radiation from other parts of the object. 4. The detector will also receive some radiation that has been scattered in the air: a. Radiation that was scattered before it reached the object, and through one or more scatterings ended up on the detector element in question. b. Both specular and diffuse reflection from other parts of the object that is not directed towards our detector element, but that is scattered onto it. Even if we shield the detector so that it can only receive radiation from a small patch of the object, components 4a and 4b will be present in addition to components 1 and 2. Correction for these effects may be of some importance in passive remote sensing applications, as the radiation is passing twice through the Earth's atmosphere. Scattering in air is usually a minor effect compared to when the density of scatterers is increased, as in liquids, tissues, and other translucent materials. We know for instance that an object that is seen through mist or fog will look blurred. And at some distance the object will disappear into the background fog. All non-metallic materials are translucent to some degree. This means that light penetrates the surface and scatters inside the material before being either absorbed or leaving the material at a different location. This phenomenon is called subsurface scattering. Even solid materials like marble display sub-surface scattering. The effect is a "softer" image than a metallic surface would give. Images of human skin, salmon fillets, or other tissue samples will not only arise from reflected light from the sample surface. Some of the radiation incident on the sample will pass through the surface, and be subject to subsurface scattering. Some of this subsurface scattering will emerge from the surface and contribute to the image. This subsurface scattering may depend on the wavelength of the light used, the directional inhomogeneities in the tissue, etc., but may also depend on the condition of the tissue. Thus, measuring subsurface scattering may be useful for quality inspection of, e.g., fish and meat.

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