From: Greg L. ® 19/11/2000 1:58:43 Subject: Rainbows post id: 172271 Since beginning my article on Atmospheric Optics, I've noticed people seem quite curious about the Rainbow. I think the processes behind this optical effect are worth examining in greater detail. I've found an excellent article in an old issue of Scientific American about this phenomenon. Unfortunately, the Scientific American website has only archived articles back to about 1993, whilst these articles were published in the 1970's. I will reproduce the sections of the article that explain what in detail a rainbow is and how theory explains what is seen in the rainbow. The single bright arc seen after a rain shower or in the spray of a waterfall is the primary rainbow. Certainly its most most conspicuous feature is its splash of colours. These vary a good deal in brightness and distinctiveness, but they always follow the same sequence: violet is innermost, blending gradually with various shades of blue, green, yellow and orange, with red outermost. Other features of the rainbow are fainter and indeed are not always present. Higher in the sky than the primary bow is the secondary one, in which the colours appear in reverse order, with red innermost and violet outermost. Careful observation reveals that the region between the two bows is considerably darker than the surrounding sky. Even when the secondary bow is not discernable, the primary bow can be seen to have a 'lighted side' and a 'dark side'. The dark region has been given the name Alexander's Dark Band, after the Greek philosopher Alexander of Aphrodisias, who first described it in about A.D. 200. Another feature that is only sometimes seen is a series of faint bands, usually pink and green alternately, on the inner side of the primary bow. These Supernumerary Arcs are usually seen most clearly near the top of the bow. They are anything but conspicuous, but they have a major influence on the development of theories of the rainbow. The first attempt to rationally explain the appearance of the rainbow was probably that of Aristotle. He proposed that the rainbow is actually an unusual kind of reflection of sunlight from the clouds. The light is reflected at a fixed angle, giving rise to a circular cone of 'rainbow rays'. Artistotle thus explained correctly the circular shape of the bow and percieved that it is not a material object with a definite location in the sky but rather a set of directions along which light is strongly scattered into the eyes of an observer. The angle formed by the rainbow rays and the incident sunlight was first measured in 1266 by Roger Bacon. He measured an angle of about 42 degrees; the secondary bow is about eight degrees higher in the sky. Today these angles are customarily measured in the opposite direction, so that we measure the total change in the direction of the sun's rays. The angle of the primary bow is thus 180 minus 42 or 138 degrees. This is called the Rainbow Angle. The angle of the secondary bow is 130 degrees. From: Greg L. ® 19/11/2000 2:20:23 Subject: re: Rainbows post id: 172273 After Aristotle's conjecture some 17 centuries passed before further signifigant progress was made on the theory of the rainbow. In 1304 the German monk Theodoric of Friedburg rejected Artistotle's hypothesis that the rainbow resulted from a collective reflection of raindrops in a cloud. He suggested instead that each drop is individually capable of producing a rainbow. Morever, he tested this conjecture in experiments with a magnified raindrop - a spherical flask filled with water. He was able to trace the path followed by the light rays that make up the rainbow. Theodoric's findings remained largely unknown for three centuries, until they were independently discovered by Descartes, who employed the same method. Both Theodoric and Descartes showed that the rainbow is made up of rays that enter a droplet and are reflected once from the inner surface. The secondary bow consists of rays that have undergone two internal reflections. With each reflection some light is lost, which is the main reason why the secondary bow is fainter than the primary one. Theodoric and Descartes also noted that along each direction within the angular rangke corresponding to the rainbow only one colour at a time could be seen in the light scattered from the globe. When the eye was moved to a new position so as to explore other scattering angles, the other spectral colours appeared, one by one. Theodoric and Descartes concluded that each of the colours in the rainbow comes to the eye from a different set of water droplets. As Theodoric and Descartes realised, all the main features of the rainbow can be understood through a consideration of the light passing through a single droplet. The fundamental principles that determine the nature of the bow are those that govern the interaction of light with transperent media, namely reflection and refraction. The law of reflection is the intuitively obvious principle that the angle of reflection must equal the angle of incidence. The law of refraction is somewhat more complicated. Whereas the path of the reflected ray is determined entirely by the geometry, refraction also involves the properties of light and the properties of the medium. The speed of light in a vacuum is invariant; it is one of the fundamental constants of nature. The speed of light in a material medium, however, is determined by the properties of the medium. The ratio of the speed of light in a vacuum to the speed of light in a substance is called the refractive index of that substance. For air the index is only slightly greater than 1, for water it is about 1.33. A ray of light passing from air into water is retarted at the boundary, if it strikes the surface obliquely, the change in speed results in a change in direction. The sines of the angles of incidence and refraction are always in constant ratio to each other, and the ratio is equal to that between the refractive indexes of the two materials. This equality is called Snell's Law, after Willebrord Snell, who formulated it in 1621. From: ? 19/11/2000 2:59:32 Subject: re: Rainbows post id: 172274 The speed of light in a material medium, however, is determined by the properties of the medium. are you implying that the speed of light changes (decreases) in anything other than a vacuum? if so, does the speed of light return to it's origional state after leaving the material medium or does it remain 'slowed down' eg: if something was travelling at the speed of light through a vacuum and then passed through an atmosphere or other material medium and then returned to a vacuum would its speed be slowed or would it still at light speed? From: Greg L. ® 19/11/2000 3:02:39 Subject: re: Rainbows post id: 172275 A preliminary analysis of the rainbow can be obtained by applying the laws of reflection and refraction to the path of a ray through a droplet. Because the droplet is assumed to be spherical all directions are equivalent and there is only one signifigant variable - the displacement of the incident ray from an vertical axis passing through the centre of a droplet. That displacement is called the Impact Parameter. It ranges from 0 when the ray coincides with the central axis, to the radius of the droplet, when the ray is tangential. At the surface of the droplet the incident ray is partly reflected, and this reflected light we shall identify as the scattered rays of Class 1. The remaining light is transmitted into the droplet (with a change in direction caused by refraction) and at the next surface it is again partially transmitted (rays of Class 2) and partially reflected. At the next boundary the reflected ray is again split into reflected and transmitted components, and the process continues indefinitely. Thus the droplet gives rise to a series of scattered rays, usually with rapidly decreasing intensity. Rays of Class 1 represent direct reflection of the droplet and those of Class 2 are directly transmitted through it. Rays of Class 3 are those that escape the droplet after one internal reflection, and they make up the primary rainbow. The Class 4 rays, having undergone two internal reflections, give rise to the secondary bow. Rainbows of higher order are formed by rays making more complex passages, but they are not ordinarily visible. For each class of scattered rays the scattering angle varies over a wide range of values as a function of the impact parameter. Since in sunlight the droplet is illuminated at all impact parameters simultaneously, light is scattered in virtually all directions. It is not difficult to find light paths through the droplet that contribute to the rainbow, but there are infinitely many paths that direct the light elsewhere. Why then is the scattered intensity enhanced in the vicinity of the rainbow angle? By applying the laws of reflection and refraction at each point where a ray strikes an air-water boundary, Descartes painstakingly computed the paths of many rays incident at many impact parameters. The rays of Class 3 are of primary importance. When the impact parameter is zero, these rays are scattered through an angle of 180 degrees, that is they are backscattered towards the sun, having passed through the droplet and been reflected from the far wall. As the impact parameter increases and the incident rays are displaced towards the center of the droplet, the scattering angle decreases. Descarted found, however, that this trend doesn't continue as the impact parameter is increased to its maximum value, where the incident ray grazes the droplet at a tangent to its surface. Instead the scattering angle passes through a minimum when the impact parameter is about 7/8 the radius of the droplet, and thereafter it increases again. The scattering angle at the minimum is 138 degrees. From: Greg L. ® 19/11/2000 3:11:19 Subject: re: Rainbows post id: 172276 This question is addressed here in the FAQ. From: Greg L. ® 19/11/2000 3:28:49 Subject: re: Rainbows post id: 172277 For rays of Class 4 the scattering angle is zero when the impact parameter is zero. In other words, the central ray is reflected twice, then continues in its original direction. As the impact parameter increases so does the scattering angle, but again this trend is eventually reversed, this time at 130 degrees. The Class 4 rays have a maximum scattering angle of 130 degrees, and the impact parameter is further increased as they bend back toward the forward scattering direction again. Because a droplet in sunlight is uniformly illuminated the impact parameters of the incident light are uniformly distributed. The concentration of scattered rays is therefore expected to be greatest where the scattering angle varies most slowly with changes in the impact parameter. In other words, the scattered light is brightest where it gathers together the incident rays from the largest range of impact parameters. The regions of maximum variation are those surrounding the maximum and minimum scattering angles, so the special status of the primary and secondary rainbow angles is explained. Furthermore, since no rays of Class 3 or 4 are scattered into the angular region between 130 and 138 degrees, Alexander's Dark Band is explained. Descartes theory can be seen more clearly by considering an imaginary population of droplets from which light is somehow scattered with uniform intensity in all directions. A sky filled with such droplets would be uniformly bright at all angles. In a sky filled with real water droplets the same total illumination is available, but it is redistributed. Most parts of the sky are dimmer than they would be from uniform scattering, but in the vicinity of the rainbow angle there is a bright arc, tapering off gradually on the lighted side and more sharply on the dark side. The secondary bow has a similar highlight, except it is narrower and all its features are dimmer. The Cartesian rainbow is a remarkably simple phenomenon. Brightness is a function of the rate at which the scattering angle changes. The angle itself is determined by two factors: the refractive index, which is assumed to be constant, and the impact parameter, which is assumed to be uniformly distributed. One factor that has no influence at all on the rainbow angle is size: the geometry of scattering is the same for small cloud droplets and for the large water-filled globes employed by Theodoric and Descartes. From: ? 19/11/2000 3:45:32 Subject: re: Rainbows post id: 172278 so if photons pass from electron to electron and this procedure causes a 'delay' in the transmission of the light wave, might this be the cause of the graduation in the colours of a rainbow - the photons that have to pass through more of the earths atmosphere might experience more delay and so they might appear slightly more 'shifted' than photons that endure less impedance? does the contour of our atmosphere contribute to the shape of the rainbow?? From: Greg L. ® 19/11/2000 3:47:25 Subject: re: Rainbows post id: 172279 So far we have ignored one of the most conspicuous features of the rainbow: its colours. They were explained of course by Newton, in his prism experiments of 1666. Those experiments demonstrated not only that white light is a mixture of colours but also that the refractive index is different for each colour. This effect is called dispersion. It follows that each colour or wavelength of light must have its own rainbow angle; what we observe in nature is a collection of monochromatic rainbows, each one slightly displaced from the next. From his measurements of the refractive index Newton calculated that the rainbow angle is 137 degrees 58 minutes for red light and 139 degrees 43 minutes for violet light. The difference between these angles is one degree 45 minutes, which would be the width of the rainbow if the rays of sunlight were exactly paralell. Allowing half a degree for the apparent diameter of the sun, Newton obtained a total width of two degrees 15 minutes for the primary bow. His own observations were in good agreement with this result. Descartes and Newton between them were able to account for the more conspicuous features of the rainbow. They explained the existence of the primary and secondary bows and of the dark band that seperates them. They calculated the angular positions of these features and described the dispersion of the scattered light into a spectrum. All of this was accomplished with only geomterical optics. Their theory however had a major failing: it could not account for the supernumerary arcs. To explain these features required a more sophisticated view of the nature of light. The supernumerary arcs appear on the inner, or lighted side of the primary bow. In this angular region two scattered rays of Class 3 emerge in the same direction; they arise from incident rays that have impact parameters on each side of the rainbow value. Thus at any given angle slightly greater than the rainbow angle the scattered light includes rays that have followed two different paths through the droplet. The rays emerge at different positions on the surface of the droplet, but they proceed in the same direction. In the time of Descartes and Newton these two contributions to the scattered intensity could be handled only by simple addition. As a result the predicted intensity falls off smoothly with deviation from the rainbow angle, with no trace of supernumerary arcs. Actually the intensities of the two rays cannot be added because they are not independent sources of radiation. From: Greg L. ® 19/11/2000 3:52:17 Subject: re: Rainbows post id: 172280 The colours of the rainbow are caused by dispersion of light of different wavelengths. In the case of the 'contour' of the atmosphere, we can assume in the case of the rainbow that it is flat, and it doesn't really enter into the equation. This article discusses how a photon interacts with a raindrop in detail, and how this contributes to the rainbow, but I haven't got to that yet. From: Greg L. ® 19/11/2000 4:08:01 Subject: re: Rainbows post id: 172281 The optical effect underlying the supernumerary arcs was discovered in 1803 by Thomas Young, who showed that light is capable of interference, a phenomenon that was already familiar from the study of water waves. In any medium the superposition of waves can lead either to reinforcement or cancellation. Young demonstrated the interference of light waves by passing a single beam of monochromatic light through two pinholes and observing the alternating bright and dark 'fringes' produced. It was Young himself who pointed out the pertinence of his discovery to the supernumerary arcs of the rainbow. The two rays scattered in the same direction by a raindrop are strictly analogous to the light passing through two pinholes in Young's experiment. At angles very close to the rainbow angle the two paths through the droplet differ only slightly, so the two rays interfere constructively. As the angle increases, the two rays follow paths of substantially different length. When the difference equals half the wavelength, the interference is totally destructive, at still greater angles the beams reinforce again. The result is a periodic variation in the intensity of scattered light, a series of alternately bright and dark bands. Because the scattering angles at which the interference happens to be constructive are determined by the difference between two path lengths, those angles are effected by the radius of the droplet. The pattern of the supernumerary bows (in contrast to the rainbow angle) is therefore dependent on droplet size. In larger drops the difference in path length increases much more quickly with impact parameter than it does in small droplets. Hence the larger the droplets are, the narrower the angular separation between the supernumerary arcs is. The arcs can rarely be distinguished if the droplets are larger than about a millimeter in diameter. The overlapping of the colours tends to wash out the arcs. The size dependence of supernumeraries explains why they are easier to see near the top of the bow; raindrops tend to grow larger as they fall. With Young's interference theory all the major features of the rainbow could be explained, at least in a qualitative and approximate way. What was lacking was a quantitative mathematical theory capable of predicting the intensity of scattered light as a function of drop size and scattering angle. From: Greg L. ® 19/11/2000 4:23:40 Subject: re: Rainbows post id: 172282 Young's explanation of the supernumerary arcs was based on a wave theory of light. Paradoxically his predictions for the other side of the rainbow, in the region of Alexander's Dark Band, were inconsistent with such a theory. The interference theory, like the theories of Descartes and Newton, predicted complete darkness in this region, at least when only rays of Class 3 and 4 were considered. Such an abrupt transition, however, is not possible as the wave theory of light requires that sharp boundaries between light and shadows be 'softened' by diffraction. The most familiar manifestation of diffraction is the apparent bending of light around the edge of an opaque obstacle. In the rainbow there is no real obstacle, but the boundary between the primary bow and dark band should exhibit diffraction nonetheless. The treatment of diffraction is a subtle and difficult problem in mathematical physics, and the subsequent development of the theory of the rainbow was stimulated mainly by efforts to solve it. In 1835 Richard Potter of the University of Cambridge pointed out that the crossing of various sets of light rays in a droplet gives rise to 'caustic' curves. A caustic, or 'burning curve,' represents the envelope of a system of rays and is always associated with an intensity highlight. A familiar caustic is the bright cusp-shaped curve formed in a teacup when sunlight is reflected from its inner walls. Caustics, like a rainbow, generally have a lighted side and a dark side; intensity increases continuously up to the caustic, then drops abdruptly. Potter showed that the Descartes rainbow ray - the Class 3 ray of minimum scattering angle - can be regarded as a caustic. All other transmitted rays of Class 3, when extended to infinity, approach the Descartes ray from the lighted side; there are no rays of this class on the dark side. Thus finding the intensity of the scattered light in a rainbow is similar to the problem of determining the intensity distribution in the 'neighbourhood' of a caustic. In 1838 an attempt to determine the distribution was made by Potter's Cambridge colleague George B. Airy. His reasoning was based on a principle of wave propogation formulated in the 17th century by Christiaan Huygens and later elaborated by Augustine Jean Fresnel. From: Greg L. ® 19/11/2000 4:43:53 Subject: re: Rainbows post id: 172283 This principle regards every point of a wave front as being a source of secondary spherical waves; the secondary waves define a new wave front and hence describe the propogation of the wave. It follows that if one knew the amplitudes of the waves over any one complete wave front, the amplitude distribution at any other point of the rainbow could be constructed. The entire rainbow could be described rigorously if we knew the amplitude distribution along a wave front in a single droplet. Unfortunately the amplitude distribution can seldom be determined, all one can usually do is make a reasonable 'guess' for some chosen wave front and hope it will lead to a good approximation. The starting wave front first chosen by Airy is a surface inside the droplet, normal to all rays of Class 3 and with an 'inflection point' (roughly, change in curvature) where it intersects the Descartes rainbow ray. The wave amplitudes along this wave front were estimated through standard assumptions based in the theory of diffraction. Airy was then able to express the intensity of the scattered light in the rainbow region in terms of a new mathematical function, known as the Airy Function. The intensity distribution predicted by the Airy function is similar to the diffraction pattern appearing on the shadow of a straight edge. On the lighted side of the primary bow there are oscillations in intensity that correspond to the supernumerary arcs; the positions and widths of these peaks differ somewhat from those predicted by Young's interference theory. Another signifigant distinction of the Airy theory is that the maximum intensity of the rainbow falls at an angle somewhat greater than the Descartes minimum scattering angle. The Descartes and Young theories predict an infinite intensity at that angle because of the caustic. The Airy theory doesn't reach an infinite intensity at any point, and at the Descartes Rainbow ray the intensity predicted is less than half the maximum. Finally, diffraction effects appear on the dark side of the rainbow; instead of vanishing abruptly, the intensity tapers smoothly within Alexander's dark band. Airy's calculations were for a monochromatic rainbow. In order to apply his method to a rainbow produced by sunlight one must 'superpose' the Airy patterns generated by the various monochromatic components. The purity of the rainbow colours is determined by the extent to which the components of the monochromatic rainbows overlap, that in return is determined by the drop size. Uniformly large drops give rise to bright rainbows with pure colours, with very small droplets giving colours that overlap so greatly that the resulting light appears almost white. From: ? 19/11/2000 4:44:32 Subject: re: Rainbows post id: 172284 if a photon is delayed by a material medium, and the more dense a medium might be, (shouldn't a proportional delay should be experienced?) then might this not have an effect within the expression of a rainbow? From: Greg L. ® 19/11/2000 5:04:22 Subject: re: Rainbows post id: 172286 The Airy theory of the rainbow has had many satisfying successes, but it contains one disturbing uncertainty-the need to guess the amplitude distribution along the chosen initial wave front. The assumptions employed in making that guess are plausible for only rather large raindrops. It is ironic that a problem as intractable as the rainbow actually has an exact solution, and one that has been known for many years. As soon as the electromagnetic theory of light was proposed by James Clerk Maxwell, it became possible to give a precise formulation of the optical rainbow problem. What is needed is a computation of the scattering of an electromagnetic plane wave by a homogenous sphere. The solution obtained was a infinite series of terms, called partial waves. A good approximation to the solution by partial wave method would require evaluating the sum of several thousand complicated terms. Computers have been employed to this task, but the labor and cost quickly become prohibitive. Also, a computer can only calculate numerical solutions, and it offers little insight into the physics of a rainbow. The first steps to a resolution of this problem were taken in the early years of the 20th century by the mathematicians Henri Poincare and G.N. Watson. They found a method of transforming the partial wave series into a rapidly convergent expression. This technique is known as the 'Watson Transformation' or the Complex Angular Momentum Method. It is not hard to see why angular momentum is involved in the rainbow problem, although it is less obvious why 'complex' values of angular momntum need to be considered. The explanation is simplest in a corpuscular theory of light, in which the beam of light is regarded as a stream of photons. Even though the photon has no mass, it does transport energy and momentum in inverse proportion to the wavelength of the corresponding light wave. When a photon strikes a water droplet with some impact parameter greater than zero, the photon carries an angular momentum equal to the product of its linear momentum and the impact parameter. As the photon undergoes a series of internal reflections, it is effectively 'orbiting' the center of the droplet. Quantum Mechanics also places additional constraints on this process. On one hand it requires that the angular momentum assumes only certain discrete values, on the other it denies that the impact parameter cannot be precisely determined. Each discrete value of angular momentum corresponds to one term of the partial wave series. From: Greg L. ® 19/11/2000 5:24:50 Subject: re: Rainbows post id: 172289 In order to perform the Watson transformation, values of the angular momentum that are conventionally regarded as 'unphysical' must be introduced. For one thing the angular momentum must be allowed to vary continously, instead of in quantized units, and it must be allowed to range over the eomplex numbers; those that include both a real component and an imaginary one, containing some multiple of sqrt(-1). The plane defined by these two components is referred to as the 'complex angular momentum plane'. Much is gained in return for the mathematical abstractions of this method. Intead of using a great many terms, one can work with a few points called 'poles' and 'saddle points' in this plane. Both poles and saddle points have a physical interpretation in the rainbow problem. Contributions from real saddle points are associated with real, ordinary light rays that we have been considering throughout this article. What about 'complex' saddle points? Imaginary or complex numbers are not meaningless solutions. In descriptions of wave propogation imaginary components are usually associated with the dampening of the wave amplitude. For example, in the total internal reflection of a light ray at a water-air boundary a light ray does 'go through the looking glass'. Its amplitude is rapidly dampened, so that the intensity becomes negligible within a depth of the order of a single wavelength. Such a wave does not propogate into the air, instead it becomes 'attached' to the interface between the water and the air, travelling along the surface, it is called an Evanescent Wave. The mathematical description of this wave involves imaginary components of a solution. 'Complex rays' also appear on the shadow side of a caustic, where they describe the damped amplitude of diffracted light rays. There are also other waves associated with 'Regge Pole' contributions to the transformed partial wave series. These waves are excited by incident rays that strike the surface of the sphere tangentially. Once such a wave is 'launched', it travels around the sphere, but is continually damped as it sheds radiation tangentially, like a garden sprinkler. At each point along the wave's circumferential path it also penetrates the sphere at the critical angle for total internal reflection, re-emerging as a surface wave after taking one or more such shortcuts. From: Greg L. ® 19/11/2000 5:31:34 Subject: re: Rainbows post id: 172291 The effect on light when it enters a different medium is that the light ray is 'bent' from the 'normal' line to a surface. This effect is called refraction, and it is important in the theory of the rainbow. Have a look at the 'Atmospheric Optical Phenomena' thread for a basic discussion of refraction or read the article I have posted carefully, as it describes how the reflection, refraction, diffraction and scattering of light rays/waves causes the rainbow to form and give rise to its observed properties. From: Greg L. ® 19/11/2000 5:42:05 Subject: re: Rainbows post id: 172292 In the simple Cartesian analysis we saw that on the lighted side of the rainbow there are two rays emerging from the same direction; at the rainbow angle these coalesce into a single Descartes ray of minimum deflection and on the shadow side they vanish. In the complex angular momentum plane, each geometric ray correspondes to a real saddle point. Hence in mathematical terms a rainbow is merely a collision of two saddle points in this plane. In the shadow region beyond the rainbow angle the saddle points do not simply dissapear; they become complex (develop imaginary components). The diffracted light in Alexander's dar band arises from a complex saddle point. It is an example of a 'complex ray' on the shadow side of a caustic curve. It should be noted that the adoption of the complex angular momentum plane method does not imply that the earlier solutions of the rainbow problem were wrong. Descartes explanation of the primary bow as a ray of minimum deflection is by no means invalid, and the supernumerary arcs can still be regarded as the produce of interference. The complex AMP method simply gives a more comprehensive accounting of the paths available to a photon in the rainbow region of the sky, and thereby achieves more accurate results. Adapted from the article 'The Theory of the Rainbow' by H. Moyses Nussenzveig, Scientific American , 1977. From: Greg L. ® 19/11/2000 6:05:59 Subject: re: Rainbows post id: 172294 I neglected to include the discussion on polarisation of light-which I will include now. An important property of light that we have so far neglected is polarization. Light is a transverse wave, one in which the oscialltion is perpendicular to the direction of its propogation. The orientation of the transverse oscillation can be resolved into components along two mutually perpendicular axes. Any light ray can be described in terms of these two independent states of linear polarisation. Sunlight is an incoherent mixture of the two in equal proportions, it is often said to be unpolarised. Reflection can alter its state of polarisation, and in that fact lies the importance of polarisation to the analysis of the rainbow. Let us consider the reflection of a light ray travelling inside a droplet when it reaches the boundary of the droplet. The plane of reflection is plane that contains both the incident and reflected rays, and provides a convient geometrical reference. The polarisation states of the incident light can be defined as being paralell and perpendicular to that plane. For both polarisations the reflectivity near the surface is slight at angles of incidence near the perpendicular, and rises very steeply near a critical angle whose value is determined by the index of refraction. Beyond the critical angle the ray is totally reflected, regardless of polarisation. At intermediate angles however, the reflectivity depends on polarisation. As the angle of incidence becomes shallower a steadily larger portion of the perpendicularly polarised component is reflected. For the paralell component, reflectivity falls before it begins to increase. At one angle in particular, reflectivity for the paralell polarised wave vanishes entirely, and that wave is totally transmitted. Hence for sunlight incident at that angle the internally reflected ray is completely polarised perpendicular to the plane of reflection. The angle is called Brewster's Angle after David Brewster, who discussed its signifigance in 1815. Light from the rainbow is almost completely polarised, as can be seen by looking at a rainbow through polaroid sunglasses and rotating the lenses around the line of sight. The strong polarisation results from a remarkable coincidence; the internal angle of incidence for the rainbow ray is very close to Brewster's angle. Most of the paralell component escapes in the transmitted rays of Class 2, leaving a preponderance of perpendicular rays in the rainbow. From: Purple ® 19/11/2000 8:57:26 Subject: re: Rainbows post id: 172307 Greg L - you just made that up ;oP From: Greg L. ® 19/11/2000 20:26:28 Subject: re: Rainbows post id: 172609 Hmm, not when it took me five hours to write the whole thing! When I'm thorough with something, I try not to leave any important details out. The polarisation of light from rainbows was interesting enough (at least in my opinion) to be included along with the other material. I think if you have polaroid sunglasses and rotate them around as you look at a rainbow, part of the rainbow would dissapear (from your point of view) as some of the incident polarised light would be cut out. If it was too detailed I apologise, but unfortuantely once I get going about something it seems natural for me to write a very long answer or series of answers. From: Martin B 20/11/2000 10:21:23 Subject: re: Rainbows post id: 172805 Hi It is worth pointing out that the colours of the rainbow are not prismatic. The monochromatic rainbow is not an infinitely bright, infinitesimally narrow strip. Instead it is a bright edge (of the reflected caustic) which then tapers off towards average reflected intensity on the inside of the bow. As a result the colours overlap and mix. The red on the outside of the bow is the purest - more mixing occurs further inside the bow. This forum is un-moderated. The views and opinions expressed are those of the individual poster and not the ABC. The ABC reserves the right to remove offensive or inappropriate messages.