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OPTOMETRY · SEMESTER 2 Thin lenses 2 Physical and Geometric Optics START READING NOTES Contents of This Topic Thin lenses 2 SUMMARY OF IMAGE FORMATION DIVERGING LENSES THE LENS EQUATION L'−L = F NEWTON’S LENS EQUATION LINEAR MAGNIFICATION POWER OF A LENS LENS SYSTEMS F = F1 + F2 Thin lenses 2 THIN LENSES II CHAPTER CONTENTS SUMMARY OF IMAGE FORMATION………………………………………………………………………………………………………………. 1 THE LENS EQUATION………………………………………………………………………………………………………………………………….. 2 NEWTON’S LENS EQUATION……………………………………………………………………………………………………………………….. 3 LINEAR MAGNIFICATION……………………………………………………………………………………………………………………………… 3 POWER OF A LENS……………………………………………………………………………………………………………………………………… 4 LENS SYSTEMS…………………………………………………………………………………………………………………………………………… 4 LENSES IN CONTACT………………………………………………………………………………………………………………………………….. 4 LENS-MAKER’S EQUATION………………………………………………………………………………………………………………………….. 5 SUMMARY OF IMAGE FORMATION CONVERGING LENSES N.B. When referring to an object position, F should be understood to be the first focal point. Similarly, F should be understood to be the second focal point when referring to an image position. We can use the graphical construction techniques of the previous chapter to analyze the nature and the position of the images obtained for various object positions. The results obtained are as follows.Thin Lenses II 5. When the object is between the lens and the focal point′, the image is formed behind the object. It is virtual, erect and larger than the object. This is how a converging lens can be used as a magnifier. Figure 5.1: Converging lenses: object between lens and focal point B. An object placed at the focal point produces an image at infinity. Figure 5.2: Converging lenses: object at focal point C. When the object is between F and 2F, the image is formed beyond 2F. The image is real, inverted and larger than the object. Figure 5.3: Converging lenses: object between focal point and twice the focal length 2F F F 2F 2F F F 2F F FThin Lenses II If we compare the situations in A and C, we see that in both cases an enlarged image is produced. However, the situation in A is preferred for the use of the lens as a magnifier, because there an ERECT image is produced. D. When the object is at 2F, we find the image at 2F. It is real, inverted and the same size as the object. (See number 5 in Problem Set 4.) Figure 5.4: Converging lenses: object distance at twice the focal length E. An object placed beyond 2F forms an image between F and 2F. It is real, inverted and smaller than the object. Figure 5.5: Converging lenses: object distance further than twice the focal length F. When the object is at infinity, the image is at F. It is again real, inverted and smaller than the object. Recall that this is how the focal point of a converging lens was defined in the previous chapter. DIVERGING LENSES In the case of a converging lens, the image is sometimes real and sometimes virtual. In a diverging lens, the image is always virtual, erect and diminished. The image is situated between the object and the lens. 2F F F 2F 2F F F 2FThin Lenses II Figure 5.6: Diverging lenses, for all object positions THE LENS EQUATION Instead of carrying out ray-tracing for each situation, we can determine the nature and position of an image by calculation instead. A simple equation relates the positions of the image and the object of a thin lens to the lens’s focal length, f. o i + = d df 1 11 Where do is the position (distance) of the object, di is the position of the image and f is the focal length. We can rewrite the equation in terms of vergence as L'−L = F L is the object vergence L’ is the image vergence F is the focal power of the lens Sign Convention Converging lenses have a positive focal length and diverging lenses a negative focal length. F FThin Lenses II NEWTON’S LENS EQUATION Newton showed that the conjugate points O and I obey the relation: x1x2 = f2 This formula states that the product of the distances of two conjugate points from the respective foci of a lens or mirror is equal to the square of the focal length. From this, it follows that x2 decreases as x1 increases. This implies that the image recedes from the focus on the right (away from the lens) when the object approaches the lens. This can be confirmed with the ray diagrams at the start of this chapter. Figure 5.7: Newton’s lens equation LINEAR MAGNIFICATION As previously stated in chapter 4, the linear magnification (m) of an optical system is the ratio between the size of the image and that of the object. A magnification of exactly 1 means that the image and the object are the same size. By “size” we mean any linear dimension such as height or width. Image Size (I) Object Size (O) m = A relationship can also be derived relating magnification to image and object distances: i o d d = = Image Size (I) m – Object Size (O) If we use the sign convention specifying that distances above the optical axis are considered positive and that distances below are considered negative, we obtain the following result: If the image is erect with respect to the object, the magnification is positive. If the image is inverted with respect to the object, the magnification is negative. The magnification is sometimes referred to as the relative size. Thin Lenses II POWER OF A LENS The power of a lens, F, is defined as the reciprocal of the focal length, in metres. The unit of power, m-1 , will be recognized as being the same as the unit of vergence, the dioptre (D). The power of a lens is thus its ability to change the vergence of a pencil of rays. The fact that vergence at a point and the power of a lens share the same units, does NOT mean that the vergence at a point equals the power of a lens. Expressed in symbols: 1 F = f LENS SYSTEMS In general, when light passes through more than one lens,

OPTOMETRY · SEMESTER 2 Thin lenses 1 Physical and Geometric Optics START READING NOTES Contents of This Topic Thin lenses 1 TERMINOLOGY OF THIN LENSES FOCAL LENGTHS F2Thin Lenses I F1Thin Lenses I IMAGE FORMATION BY GRAPHICAL CONSTRUCTION DIVERGING LENS LINEAR MAGNIFICATION Object Size (O) CONJUGATE POINTS Thin lenses 1 THIN LENSES I CHAPTER CONTENTS TERMINOLOGY OF THIN LENSES………………………………………………………………………………………………………………… 1 FOCAL LENGTHS ………………………………………………………………………………………………………………………………………… 0 REAL AND VIRTUAL …………………………………………………………………………………………………………………………………….. 2 IMAGE FORMATION BY GRAPHICAL CONSTRUCTION …………………………………………………………………………………. 2 LINEAR MAGNIFICATION……………………………………………………………………………………………………………………………… 5 CONJUGATE POINTS…………………………………………………………………………………………………………………………………… 5 TERMINOLOGY OF THIN LENSES A thin lens is one whose thickness is very small in comparison to its focal length1 . A typical thin lens consists of a piece of glass or plastic, ground so that each of its two refracting surfaces is a portion of either a sphere or a plane. A lens is used to direct or control rays of light. The refraction of light at the surface of a lens depends on its shape, its index of refraction, and the nature of the medium surrounding it (usually air), in accordance with Snell’s Law. Lenses are commonly used to form images by refraction in spectacles and in optical instruments such as cameras, telescopes and microscopes. 1 Although any contact lens must be considered a thick lensThin Lenses I Lenses can be placed in two groups. Those in the one group are thicker at the centre than at the rim. They are known as converging lenses (or convex lenses). They refract incident parallel rays so that they converge at a point on the opposite side of the lens. The others are thinner at the centre than at the rim. They are known as diverging or concave lenses. They refract incident parallel rays so that they appear to diverge from a point located on the incident side of the lens. Any object viewed through such a lens always appears erect and smaller than when viewed with the unaided eye. A meniscus (meaning crescent-shaped) lens has one convex surface and one concave surface. The principal axis or optical axis of a lens is the line joining the centres of curvature of the two surfaces. Rays making small angles with the optical axis are referred to as paraxial rays. The optical centre of a thin lens is such that any ray passing through that point is not deviated. For the cases we will deal with in this course, the optical centre of a lens can conveniently be thought of as the geometric centre of the lens. Figure 4.1: Different types and shapes of lenses FOCAL LENGTHS There are two points on the optical axis which need special attention. The following figure shows a pencil of paraxial rays from an object at an infinite distance from a converging lens. As such, the pencil will be effectively parallel on reaching the lens. These rays are refracted through the point F2 which is called the second principal focus or second focal point of the lens. The distance from the optical centre to F2 is called the second focal length of the lens and will be referred to by the symbol f2. Figure 4.2: Illustration of the second focal point of a converging lens Similarly, in the next figure, there is the point F1 from which paraxial rays, after refraction by the lens, emerge parallel to the axis. F1 is referred to as the first principal focus or first focal point of the lens, and the distance from the optical centre to F1 is referred to as the first focal length of the lens and is given the symbol f1. F2Thin Lenses I Figure 4.3: Illustration of the first focal point of a converging lens If the lens is thin, and the medium on each side of the lens is the same, then the numerical values of f1 and f2 will be identical. Note that the diagrams show lenses with exaggerated thicknesses and rays that make greater angles with the optical axis than should be the case for paraxial rays. This has been done simply to allow the clear exposition of the refraction at each surface. When “the focal length” of the lens is stated without specifying it to be the first or second focal length, it must always be inferred that this means the second focal length of the lens. In the case of a diverging lens, there are two similar principal foci. The next figure shows the point F1, the first principal focus or first focal point of a diverging lens. Rays directed towards this point emerge from the lens parallel to the optical axis. Once again, the distance from the optical centre to F1 is the first focal length, f1. F1 can be seen to be on the opposite side of the lens compared to the incident light. Figure 4.4: Illustration of the first focal point of a diverging lens Similarly, the second principal focus or second focal point (designated F2) is formed where rays that are incident on a diverging lens parallel to the optical axis appear to diverge from. The distance from the optical centre to F2 is thus the second focal length of the lens. The figure shows that the second focal point lies on the same side as the incident light. As before, if the lens is thin and the media on each side of the lens are identical in refractive index, then the focal lengths have the same magnitude. F1 F1Thin Lenses I Figure 4.5: Illustration of the second focal point of a diverging lens REAL AND VIRTUAL The major usefulness of lenses is their ability to form images of an object. The object may be self-luminous, giving off its own light (like the sun or a light bulb), or it may reflect the light that falls on it (like an apple or a page of this book). In either case, an image of the object is formed where light rays that come from points on the object intersect or at the points from which

OPTOMETRY · SEMESTER 2 Refraction Physical and Geometric Optics START READING NOTES Contents of This Topic Refraction WHAT IS REFRACTION? REFRACTING MATERIALS THE REFRACTIVE INDEX AIR OTHER MEDIUM THE REFRACTIVE INDEX VARIES WITH WAVELENGTH REAL AND APPARENT DEPTH TOTAL INTERNAL REFLECTION USES OF TOTAL INTERNAL REFLECTION WHITE LIGHT IS POLYCHROMATIC DISPERSION THE FOLLOWING DERIVATION IS NOT FOR EXAMINATION PURPOSES. COLOUR SELECTIVE TRANSMISSION PRIMARY, SECONDARY & COMPLEMENTARY COLOURS Red 700 – 635 PIGMENTS, PAINTING AND PRINTING OPTICAL PATH LENGTH REFRACTION AT CURVED SURFACES = ̶ 5.88 D = ̶ 6.46 D Refraction REFRACTION CHAPTER CONTENTS REFRACTING MATERIALS …………………………………………………………………………………………………………………………… 0 WHAT IS REFRACTION?………………………………………………………………………………………………………………………………. 0 THE REFRACTIVE INDEX …………………………………………………………………………………………………………………………….. 1 THE REFRACTIVE INDEX VARIES WITH WAVELENGTH ……………………………………………………………………………….. 2 REFRACTION AT PLANE SURFACES……………………………………………………………………………………………………………. 2 REAL AND APPARENT DEPTH……………………………………………………………………………………………………………………… 3 TOTAL INTERNAL REFLECTION…………………………………………………………………………………………………………………… 4 USES OF TOTAL INTERNAL REFLECTION……………………………………………………………………………………………………. 5 WHITE LIGHT IS POLYCHROMATIC ……………………………………………………………………………………………………………… 6 DISPERSION ……………………………………………………………………………………………………………………………………………….. 8 COLOUR…………………………………………………………………………………………………………………………………………………….12 OPTICAL PATH LENGTH……………………………………………………………………………………………………………………………..15 REFRACTION AT CURVED SURFACES ……………………………………………………………………………………………………….15 LENS CLOCK II……………………………………………………………………………………………………………………………………………16Refraction WHAT IS REFRACTION? When a ray of light in air is incident on the surface of a transparent medium such as glass, some of it is reflected, whilst the remainder is transmitted. The larger the angle of incidence is, the larger the amount of light that is reflected. No medium is perfectly transparent and some absorption of light always occurs, the energy being converted to heat. This latter effect will be ignored. The direction of the ray inside the medium is different to that of the incident ray unless the incident ray is normal (perpendicular) to the surface. The transmitted ray is bent as it crosses the surface between one medium and another. This change of direction of the ray at the surface is called refraction. Figure 3.1: Refraction at the air/water and water/air interfaces The preceding diagrams show several important aspects of refraction. When a light beam goes from air into water along the normal to the surface between them, it simply continues along the same path. When it enters the water (an optically more dense medium) at any other angle, it is bent towards the normal. The paths are reversible; thus a light beam emerging from the water (into the optically less dense air) is bent away from the normal as it enters the air. This effect gives rise to the phenomenon of the apparent depths of objects. REFRACTING MATERIALS Common refracting materials are glass, (in particular high-grade optical quality glass), quartz, and a variety of plastics. These have been chosen not only for their effect on the direction of light rays passing through them, but also for their transparency, homogeneity, and their resistance to atmospheric corrosion. Optical glass is commonly used in the manufacture of prisms and lenses. Two main types of optical glass are available: these are crown and flint. The former is a compound of silica (sand, SiO2) and salts of sodium and potassium. In addition, small quantities of other materials such as barium and zinc oxides may be present. Flint glasses, in addition to the constituents above, contain oxides of lead and are denser than crown glasses. Certain plastics materials are now increasingly being used for ophthalmic lenses. In this category is the thermosetting material allyl diglycol carbonate, commonly known as CR-39 (the CR standing for Columbia Resin). These plastics start as linear polymer chains that get cross-linked permanently during molding. Therefore they cannot be remolded. Polyethylene, polystyrene, polyvinyl chloride and polytetrafluoroethylene (PTFE) are examples of thermoplastic materials. These plastics do not undergo any chemical change during the molding process and can therefore be remolded several times without changing their properties. AIR WATER AIR WATERRefraction THE REFRACTIVE INDEX Refraction occurs because light travels at different speeds in different media. We have previously noted that the speed of light in vacuum, c, equals 3 x 108 m/s, which is the maximum speed at which light travels. (We will assume that the light travels with the same speed in air.) In a material medium, the speed of the light, v, is less. The ratio of these speeds is the refractive index (n) of the medium. c n = v Since v is never greater than c, the index of refraction (which is a dimensionless number) is never less than 1. The index of refraction is sometimes called a measure of the optical density of the material. Materials with larger indices of refraction are said to be optically denser. The previous statements about the direction in which light rays are bent in passing into a different medium can now be restated in terms of optical density. In order to account for the light slowing down as it does, consider the accompanying figure which represents a beam of light entering a piece of glass from the left. Once inside the glass, the light may encounter an electron bound to an atom, indicated as point A in the figure. Let us assume that light is absorbed by the atom, which causes the electron to oscillate. The oscillating electron then acts as an antenna and radiates the beam of light toward an atom at point B, where the light is again absorbed by an atom at that point. (We need not consider the details of these absorptions and emissions.) For now, it is sufficient to think of the process as one in which the light passes from one atom to another through the glass. (The situation is somewhat analogous to a relay race in which a baton is passed between runners on the same team.) Although light travels from one atom to another with a speed of 3 x 108 m/s, the processes of absorption and emission of light by the atoms take time. Enough time is required, in fact, to lower the speed of the light in the medium. Once the light emerges into the air again, the absorptions and the emissions cease and its speed returns to the original value. Figure 3.2: A beam of light entering a piece of glass The frequency of a light wave is determined by its

OPTOMETRY · SEMESTER 2 Vergence Physical and Geometric Optics START READING NOTES Contents of This Topic Vergence DEFINITION SIGN CONVENTION AND UNITS CALCULATING VERGENCE CURVATURE OF WAVEFRONTS EFFECTIVITY APERTURE, RADIUS OF CURVATURE AND SAGITTA LENS CLOCK I Vergence VERGENCE CHAPTER CONTENTS DEFINITION…………………………………………………………………………………………………………………………………………………. 1 SIGN CONVENTION AND UNITS…………………………………………………………………………………………………………………… 2 CALCULATING VERGENCE………………………………………………………………………………………………………………………….. 3 CURVATURE OF WAVEFRONTS ………………………………………………………………………………………………………………….. 4 EFFECTIVITY ………………………………………………………………………………………………………………………………………………. 5 APERTURE, RADIUS OF CURVATURE AND SAGITTA …………………………………………………………………………………… 7 LENS CLOCK I……………………………………………………………………………………………………………………………………………… 8 DEFINITION Much of the work in geometrical optics is concerned with the convergence and divergence of pencils of light rays. In fact, the main purpose of spectacle lenses is to alter the extent of convergence or divergence of light rays before they enter the eye. The convergence or divergence of a pencil of light rays may be expressed by the general term vergence. The vergence at a particular point in a pencil of rays travelling in air is the reciprocal of the distance from the point to the source or the focus. Clearly, we will be dealing with a source in the case of a diverging pencil and a focus in the case of a converging pencil. From the definition, it follows that the closer the point in question is to the source (or focus), the larger the vergence, and vice versa.Vergence The definition of vergence stated above does not distinguish between those points which are situated in converging pencils of rays and those points which are situated in diverging pencils. In order to be able to distinguish between diverging and converging pencils, when studying the effects of optical components such as lenses, a sign convention must be employed. A sign convention is a set of definite rules such that the value of any distance measured on an optical diagram may be given a positive or a negative sign, corresponding to convergence and divergence respectively. SIGN CONVENTION AND UNITS The sign convention for vergence is as follows. 1. In optical diagrams, light is assumed to travel from the left to the right in a positive direction. If the distance from the point in question to the source or focus is measured in the same direction as that in which the rays of light are directed, the numerical value of the distance is given a positive sign (+). 2. If the distance from the point in question to the source or focus is measured in the opposite direction to that in which the light is travelling, the magnitude of the distance is given a negative sign (−). Refer to the below figures. The distance from the point D to the source is measured in the opposite direction to the direction in which the light is travelling and we must apply a minus sign to the distance d. Hence, the vergence at D (= 1/d) will be a negative value. Figure 2.1: Diverging pencil of rays. The distance d is measured from the point to the source, hence from right to left leading to a negative value. However, the distance from the point C to the focus is measured in the same direction as the direction in which the light is traveling and the value of the distance cis assigned a plus sign. Therefore, the vergence at C (= 1/c) will be a positive value. Figure 2.2: The distance c is measured from the point to the focus, from left to right, leading to a positive value.Vergence These rules result in the important conclusion that at any point in a converging pencil of rays the value of the vergence of the light is positive, and at any point in a diverging pencil of rays the value of the vergence of the light is negative. It also follows that at any point in a parallel pencil of rays, for which the source or the focus may be considered to be at infinity, the vergence will be derived as follows: 1 vergence = = 0 ±∞ That is, at any point in a parallel pencil of rays, the value of the vergence of the light is zero. If the distance from a point in a pencil to the source or focus is expressed in metres, then the value of the vergence at that point is expressed in dioptres. We can define one dioptre, symbol 1 D, as being the magnitude of the vergence in a pencil of rays in air, at a point one metre from the source or the focus. CALCULATING VERGENCE Figure 2.3: a) Diverging pencil of rays b) Converging pencil of rays Refer to the previous diagrams of which (a) shows a diverging pencil and (b) shows a converging pencil of rays. The point from which the diverging pencil of rays actually originates will now be referred to as an object. In optics, the distance from a point such as A to an object is represented by the symbol l. Thus the distance from A to the object = l where l is measured in metres. The vergence at A is 1/ l and this is given the symbol L (dioptres). 1 L(dioptres) = l (metres) The point through which all the converging rays pass will be referred to as an image. We will represent the distance from a point such as B to an image by l as well. Care must be taken to apply the sign convention in order to find the correct sign for the vergence. The vergence at B will then also be given by the above equation. For any optical medium with an index of refraction n, the vergence of the light travelling through the medium is given l n L =Vergence It is worth emphasizing that the dioptre unit is really the reciprocal metre (m-1 ). The dioptre is merely a unit of convenience which is easier to say than ‘reciprocal metre’, but when considering units in some equations it will be necessary to think in terms of reciprocal metres. The name dioptre was chosen from dioptrics, the name given to the branch

OPTOMETRY · SEMESTER 2 Nature of light Physical and Geometric Optics START READING NOTES Contents of This Topic Nature of light THE NATURE OF LIGHT LIGHT WAVES VISIBLE LIGHT Wavelength: Long Short Meets Microwave THE SUN’S RAYS THE RAY APPROACH A DIVERGING PENCIL Air 1.001 PHASE DIFFERENCE Nature of light NATURE OF LIGHT CHAPTER CONTENTS THE NATURE OF LIGHT……………………………………………………………………………………………………………………………….. 1 LIGHT WAVES……………………………………………………………………………………………………………………………………………… 3 VISIBLE LIGHT …………………………………………………………………………………………………………………………………………….. 5 THE RAY APPROACH ………………………………………………………………………………………………………………………………….. 7 REFRACTIVE INDEX ……………………………………………………………………………………………………………………………………. 9 PHASE DIFFERENCE…………………………………………………………………………………………………………………………………… 9 THE NATURE OF LIGHT Until the beginning of the 19th century, light was considered to be a stream of particles, emitted by a light source, which stimulated the sense of sight on entering the eye. The chief architect of the particle theory of light was Newton. With this theory, he provided simple explanations of some known experimental facts concerning the nature of light, such as the laws of reflection and refraction. According to Newton, the particles emitted by a source travelled in a straight line until the boundary of a new medium was encountered. He derived a relationship that predicted that the speed of light in a medium such as water would be greater than its speed in air. This is exactly the opposite of the result predicted by the wave theory. Foucault later found a value for the velocity of light in a medium that showed that Newton’s prediction was incorrect. This played a large part in discrediting the socalled corpuscular theory of light.Nature of Light Most scientists initially accepted Newton’s particle theory of light. However, during Newton’s lifetime, another theory was proposed. In 1678, a Dutch physicist and astronomer, Christian Huygens (1629-1695), showed that a wave theory of light could also explain the laws of reflection and refraction. In addition, his theory could account for the fact that light entering a medium from air at an angle would be bent. The wave theory did not receive immediate acceptance for several reasons. All the waves known at the time (e.g. sound and water waves) travelled through some sort of medium; but light from the Sun could travel to Earth through empty space. Furthermore, it was argued that if light were some form of wave, it would bend around obstacles; hence, we should be able to see around corners. It is now known that light does indeed bend around the edges of objects. This phenomenon, known as diffraction, is not easy to observe because light waves have such short wavelengths. Even though experimental evidence for the diffraction of light had been discovered by Francesco Grimaldi (1618- 1663) around 1660, for more than a century most scientists rejected the wave theory and adhered to Newton’s particle theory. This was partly due to Newton’s great reputation as a scientist. The first clear demonstration of the wave nature of light was provided by 1801 by Thomas Young (1773-1829), who showed that under appropriate conditions, light exhibits interference behaviour. That is, at certain points in the vicinity of two sources, light waves can combine. They can even cancel each other by destructive interference. Such behaviour could not be explained by a particle theory. A few years later, and building on Young’s experimental work, Augustin Fresnel (1788-1827) definitely signalled the end of 18th century physics and the birth of modern optics. He extended the wave theory of light to a large class of optical phenomena and developed the theoretical framework that became the foundation of modern optics. The most important development concerning the theory of light was the work of James Clark Maxwell, who in 1865 predicted that light was a form of high-frequency electromagnetic wave. His theory predicted that these waves should have a speed of 3 x 108 m/s. This value is in agreement with the experimentally measured speed. Light is transmitted in the form of transverse waves. In the diagram below we see that the electric and magnetic vectors associated with an electromagnetic wave are at right angles to each other and also to the direction of wave propagation. Figure 1.1: Schematic diagram of an electromagnetic wave propagating in the x direction. The electric field vector E vibrates in the xy plane, and the magnetic field vector B vibrates in the xz plane Although the classical theory of electricity and magnetism explained most known properties of light, some subsequent experiments could not be explained by the assumption that light was a wave. The most striking of these was the photoelectric effect, discovered by Hertz. Hertz found that clean metal surfaces emit charges when exposed to ultraviolet light. In 1905, Einstein published a paper that formulated the theory of light quanta and accounted for the photoelectric effect. He reached the conclusion that light is composed of corpuscles, or discontinuous quanta of energy. Furthermore, he asserted that light interacting with matter also consists of quanta, and he brilliantly worked out the implications of the photoelectric process. Nature of Light More specifically, Einstein showed that the energy of a photon is proportional to the frequency of the electromagnetic wave: E = h·f where h= 6.63 x 10-34 Js is Planck’s constant. This theory contains features of both the wave and particle theories of light. In view of these developments, light must be regarded as having a dual nature. That is, to best describe light’s behaviour, we need in some cases to consider light to be acting as a wave and in others to be acting as a particle. For example, classical electromagnetic wave theory provides adequate explanations of light propagation and of the effects of interference, whereas the photoelectric effect is best explained by assuming that light is a particle. The nature we consider light to have in a particular situation will depend on which is the most appropriate model for those circumstances.. . In this course, we consider Physical Optics which involves phenomena which can only be explained by reference to the nature of light, as well as phenomena which do not depend on the nature of light, but only on its path. This