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Light: Level I Light: 7) Spectrum and Colors Light and Color Spectrum Electromagnetic Spectrum Mixing of Spectral Colors Mixing of Pigments 8) Rectilinear Propagation and Reflection of Light: Sources of Light Nature of Light Rectilinear Propagation of Light (i.e., Light travels in a straight line) Effects of Rectilinear Propagation of Light Formation of Eclipse Light Reflection from a Plane Surface Multiple Reflection 9) Spherical Mirrors Concave & convex mirrors Convergence & divergence of light Reflection of light from spherical mirrors Uses of mirrors Chapter 7: Spectrum and Colors Spectrum and Colors Light and Color Spectrum Electromagnetic Spectrum Mixing of Spectral Colors Mixing of Pigments Light and Color These are two beautiful pictures of sunrise. What do see in it? In first picture as the sun comes up completely, there is bright light. We see some rays, a bright patch of water, and some scattering from the clouds also. Though the light is bright, it is not fully white; there is yellowish color in the sky. In second picture the situation is again beautiful but different. Sun is just rising. The yellowish semicircle indicates the position of the sun. The clouds above are red-orange. Its reflection exists over the total spread of water. Above the red clouds, there are gray, bluish grey clouds. The combination is awesome and unique. One must see sunrise in a partially cloudy day to enjoy colorful combinations. Above four pictures are the pictures of sunset. In first picture, yellow is near setting sun. There is combination of orange, pink and violet. Second picture contains outstanding shades of grey. The moon ark, its reflection along with reflection of sun, the black part show remarkably unique combination. Third picture is combination of yellow, orange and bluish green. The last one contains white spot of the sun, yellow surrounds it. Orange spreads are horizontal while violet, blues are like rays. We see all colors in the sky. You need to enjoy them at sunrise or sunset. Partial cloudy days are still better. Whitish clouds or thick black clouds with water make different colorful combinations in the sky. Activity: Wake up early morning, at least half an hour to 45 min before the sunrise. Enjoy various color combinations in the sky. Observe the changes in colors with time. Make time slots of five minutes. Make a table of these time slots and prominent colors in the sky. Observe the sunset as far as on the same day. Observe the changes in colors in different time slots just as in the morning. Make another table of the evening. Compare the two tables. Note it totally depends on your position, cloud combination on the day, nature of clouds, etc. Activity: You pursue this activity only if your family possesses a digital or mobile camera. Else wait for few days; you can do it in later years in your life. Take couple of good pictures, one of sunrise and one of sunset. Upload and insert it in your own text/notes in context of learning this chapter. Make your learning participative. Share it with your friends. Are the colors and white light related? This was the question Isaac Newton asked himself. http://www.youtube.com/watch?v=uLQjQ64299s (If you want to repeat the video then drag the curser to original position and play) Isaac Newton prepared a wheel of seven colors. He rotated the disc whose speed can be increased gradually. He rotated the disc by hand, manually. The colors started wearing out. At a particular speed all colors practically vanished and disc appeared whitish. With the help of this simple experiment he proved that ‘light is composed of seven different colors.’ He further proved his statement by passing a ray of white light through a prism. The actual ray passing through prism is shown in the second figure. This is a photograph of experimental situation. The first figure is the schematic diagram that shows the process. A ray of light enters the glass prism. As the light enters in a denser glass medium, the velocity of light reduces. The velocity for each color is different. As a result each color undergoes different deviation. In prism each color travels in different direction. When each color enters in air medium again from the other end, each color deviates further. The out coming light is arrangement of colors in a proper order VIBGYOR. This separation of colors from original white light proves that ‘light is composed of different colors.’ Activity: Go in a laboratory of your school. Request your teacher to show the spectrum. Write down the process how you obtained a spectrum, and about your experience after seeing it. Toy top: The above top possesses a disc with colors. When the top is rotated slowly the colors start mixing. If the top is rotated fast, then it looks like second photograph. Why it is so? The answer lies in persistence of vision. If any image is formed on the retina, the image remains on the retina for 0.1 second. If the speed exceeds this ‘limiting speed’ then all colors mix in each other producing white color. Activity: Purchase a top from a local toy shop. See that it has the disc with conical shape below. Take a plane paper. Mark a circle of the same diameter of the disc of the top. Paint a disc like this. Paste it on the plane disc of the top. Rotate the top as fast as you can. You will see the mixing of colors as seen in the second diagram. Assignment: A disc is divided in seven sectors. Each sector is colored by different color. What should be minimum number of rotations per minute so that the disc will appear white? http://faculty.washington.edu/chudler/benham.html Spectrum: We have seen that when a ray of light passes through a prism, it splits in its constituents. The colors separate and arrange themselves in order. They get arranged with decreasing wavelength (or increasing frequency) from top to bottom. The topmost color is red having longest wavelength and lowest frequency. While violet is at the bottom having shortest wavelength and highest frequency. The color sequence is conventionally read from bottom to top as VIBGYOR. This VIBGYOR, the ordered arrangement of colors is called a spectrum of light. We have seen the spectrum in above diagram obtained from the prism. In following diagram the first one is the continuous spectrum. The source is like amorphous hot body. The colors gradually change having no sharp boundaries. The second one is the emission spectrum of element. Hot material is in exited state. It emits typical wavelengths. They are the bright lines of specific wavelengths on dark background. These specific wavelengths are characteristic wavelengths of that element. The third spectrum is the ‘absorption spectrum’. This spectrum has the ‘absent’ lines on continuous background. The white lines represent the absorbed energies by the element. It lower diagram blue material represents absorbing medium. Following is the emission spectrum of iron. http://www.youtube.com/watch?v=9eEyTw4wylk http://web.mit.edu/22.51/www/Extras/color_theory/color.html Electromagnetic spectrum and visible light: Light is electromagnetic wave in nature. Light wave is composed of huge number of photons. Photon is fundamental energy quantum (bunch). It has dual nature, particle as well as wave. We will study all this later in details. In this article, we will see various ranges, their names of electromagnetic spectrum. The diagram shows ‘Electromagnetic spectrum’ with visible light highlighted. We see the ranges of frequency and wavelength better in following diagram. Generally, the electromagnetic spectrum is classified by wavelength into radio, microwave, infrared, the visible region that we perceive as light, ultraviolet, X-rays and gamma rays. The visible region has limitation due to ‘limitation of ability of human eye’. The behaviour of EMR (Electro-Magnetic Radiation) depends on its wavelength. Higher frequencies have shorter wavelengths, and lower frequencies have longer wavelengths. When EMR interacts with single electron, its behaviour depends on the amount of energy per quantum it carries. The visible light is formed of small packets of energy. These energy packets are called as energy quanta or photons. Photons have characteristic energy (E= hν). Photons can interact with atoms and molecules causing electronic excitation within atoms and molecules. Sometimes energetic photons may cause the electrons to eject out of the atom or molecule. We see one color for many wavelengths. i.e. for all wavelengths from 620nm (6200AU) to 750nm(7500AU) we see red color. Hence we say each color has a range of wavelengths rather than one wavelength. Following is the table that gives colors and their wavelength ranges. Color Frequency Wavelength violet 668–789 THz 380–450 nm blue 606–668 THz 450–495 nm green 526–606 THz 495–570 nm yellow 508–526 THz 570–590 nm orange 484–508 THz 590–620 nm red 400–484 THz 620–750 nm It has been proved that the visible spectrum of some animals is different than human eye. The snakes can see in infrared region. This is because their retina is capable of thermal imaging. Mixing of Spectral Colors: http://www.yorku.ca/eye/thejoy1.htm How We See Color Observe neatly, one can see the inverted image formed on the retina. The above diagram of the eye is most beautiful diagram. It clearly shows the retina and the network of the nerves behind it. The network of nerves contains the cones and rods. Fig 2 shows structure of cones and rods. Each cone and rod has the set of neurons. Lower nerve cells also have a set of neurons. If we keenly observe, the neurons do not physically touch each other. The signal p.d. gets induced and the signal transfers from one cell to next. Finally the signal is carried to brain where we sense the color, contrast and details of the object. If cones see color, what do rods do? The rods in our eyes perceive contrast, so highlights and shadows are always relative values. The checks that we see are actually shades of grey. The contrast is seen due to the rods. Additive color mixing involves multiple sources of light with different colors in each source. The above diagram is obtained using three spot lights with red, blue and green filters. These filters are expected to transmit the midfrequency or midwavelength of the respective range of the color. We then get the above diagram. Primaries of Light: Red, Green and Blue are called as the primary colors. We have already seen that mixing of all seven colors yield white light. If red, green and blue are mixed then we get white light. It is seen in the above diagram. We also see that Red + Blue = Magenta Red + Green = Yellow Green + Blue = Cyan Magenta, Yellow and Cyan are called as the ‘complementary colors’. The meaning of ‘complementary colors’ is clear from the following equation like statements. Green + Magenta = White Blue + Yellow = White Red + Cyan = White Red, Blue and Green are (single and) primary colors. By mixing ‘one’ more (respective complimentary) color to each of them, we get the white color. It means each complementary color is a mixture of ‘six’ remaining colors for that respective primary color. Mixing of Pigments Let us learn the difference in primary color and ‘pigment’. Primary colors are the sources of light. Pigments are actual materials, actual compounds existing in nature. Let us be more explicit. Suppose we have a source of green light and a source of white light. We have a darkroom. We shine a green source on white paper and also on a green leaf. Both appear green. Now we shine a white source on a white paper and a green leaf. Now the paper will appear white while the leaf appears as ‘green’. To explain this event we say ‘the leaf appears as green because it is green by its nature’. We accept this explanation because we have been seeing the leaves green and we are used to it. Actually the material (chlorophyll) in the leaf reflects green light and absorbs remaining all colors present in white light. Therefore material in leaf, the chlorophyll is a ‘pigment’. In white light, a pigment appears as one color because it reflects the color you see and absorbs the colors which you do not see. In other words, pigments produce a color by subtracting other colors from white light. The color you see is the difference between white light and the colors that were absorbed. Hence, if we have to understand the pigments we must understand the absorptive properties of colored materials or what happens when pigments are added. Secondary system of colors: Secondary colors of one system serve as the primary colors for the other. i.e. If yellow, magenta and cyan are ‘considered as the primary’ colors then we get red, blue and green as ‘their’ complementary colors. But in second system i.e. if yellow, magenta and cyan all three are mixed then we get the ‘black’. This is because ‘cyan’ contains blue and green. Cyan eliminates rest five colors including red. Magenta eliminates five including green. Yellow eliminates blue and other four. This way all colors get eliminated when cyan, magenta and yellow are added. We therefore get black. Thus Cyan, Magenta and Yellow are ‘pigments’ in a system of colors where Red, Green and Blue are primary. Subtractive color mixing involves a single source of light with different colors absorbing various wavelengths of the color spectrum. Comparison of Additive and Subtractive Primary Colors It is clear from the above diagram that color diagram and pigment diagram are complementary to each other. Color printing requires preparing various colors. These colors are prepared by adding pigments, i.e. colors are prepared by ‘subtracting of light’ method. Black ink is added to make a given color dark. Black color is represented as ‘K’. This model of making colors is called as ‘CMYK’ model. http://www.teachersdomain.org/asset/lsps07_int_lightpigment/ Pigment powders are inert colorant with no binding power of their own. To use pigments, a binder or sealer must be employed to allow them to adhere to a surface. This is achieved either by mixing pigments into a binding medium (such as paint). They can also be suspended into translucent or transparent materials. Since inorganic pigments are inert, they will not chemically react with other materials. Therefore they can be used in water, oil or chemical based products. There is a distinct difference between pigments and dyes. A dye will dissolve within a medium whereas a pigment disperses in the medium as very fine particles. Hence dyes form uniform solutions and spread uniformly while pigments form colloidal solution and spread nonuniformly. The amount of pigment to be added into a base depends upon the color desired (expected) and the medium used. Each medium has a limit. This is the maximum amount of pigment that can be added to the medium to obtain best binding quality (i.e. mechanical stability). This limit varies from medium to medium. Activity: i) Purchase red, green and blue colored powders from the local market. Also purchase black power. Test the softness of each powder. This can be done by taking a pinch of a powder and rub it in two fingers. You can test the softness. Softness of all colors should be approximately same. Take one unit approximately 30g of one color say blue. Add 5g of black powder to it. Mix it thoroughly. Compare the color of original blue and this new color. What do you observe? Does it confirm what you have learnt? Activity ii): Add two primary colors say blue and red? Take 20g of each powder. Mix it thoroughly. Which is the color that you get? Note it down. 8) Rectilinear Propagation and Reflection of Light: Sources of Light Nature of Light Rectilinear Propagation of Light (i.e., Light travels in a straight line) Effects of Rectilinear Propagation of Light Formation of Eclipse Light Reflection from a Plane Surface Multiple Reflection Rectilinear Propagation and Reflection of Light: Sources of Light: http://www.youtube.com/watch?v=8jkTBTDIhJ8 We have seen some pictures of sources of light. Early man must have noticed that ‘sun’ is main source of light. Stars that we see in the night are also sources of light. Today, we know that planets revolving around the sun are not the sources of light. Moon is planet of Earth. It also is not a source of light. It is a reflecting body. It looks big and bright in night because it is comparatively nearer to the earth. When we use a word ‘light’, it is ‘visible light’. Light is electromagnetic radiation that is visible to the human eye. Light is responsible for the sense of sight i.e. we can see because of light. Visible light has a wavelength in the range of about 380 nanometres (nm), or 380×10−9 m, to about 740 nanometres. This range is between invisible infrared having longer wavelengths and the invisible ultraviolet having shorter wavelengths. A typical "light source" emits electromagnetic radiation in the visible spectrum. Man used animal fat in candle as a source of light. Later kerosene and oil dug out from earth were used as light sources. Electricity was discovered in late nineteenth century and incandescent light were invented by Edison in early twentieth century. Later fluorescent light, CFL and LEDs are discovered. Man has designed enormous number of lamps and lamp shades as per need and necessity. Nature of Light: Corpuscular theory of light was originally proposed by Pierre Gassendi. It states that light is made up of small discrete particles called "corpuscles" (little particles). They travel in a straight line with a finite velocity and possess kinetic energy. It was largely developed by Sir Isaac Newton. It was later known as Newton’s Corpuscular theory. Newton proposed that light is shot out from a source as a stream of particles. He stated that particles of different colors should be of different sizes, the red particles being larger than the blue. He further argued that particles which cause red color have larger inertia, because it has larger mass. It bends less. The violet particles are lighter and possess less inertia. Hence they bend more. According to Newton's theory, sources of light continuously emit corpuscles. The mass of the source must be reducing constantly. Newton's theory was able to explain laws of reflection and laws of refraction to some extent. Reflection was explained as follows. The elastic ball bounces off the smooth surface. He also tried to explain refraction. The massive particles are attracted by the transparent medium. They get pull by the medium; hence the ray bends towards the normal. When the particle is deep inside the medium, it does not experience any pull. Once the ray is bent at the interface, the ray continues to travel in straight line. As the ray leaves the denser medium, again the pull makes it bend away from the normal. Newton's theory remained in force for more than 100-200 years. It was considered better than Huygens' wave front theory. It was partly because of Newton’s great prestige. However when the corpuscular theory failed, Huygen’s wave theory adequately explained the diffraction, interference and polarization. www.youtube.com/watch?v=uO2uyvf-E3k Wave Theory of Light Huygen proposed that light behaves like a wave. Light waves are electromagnetic waves. They are transverse in nature. They are made up of both electric ( ⃗ and magnetic ( ⃗ ) fields. ( ⃗ and ( ⃗ ) fields oscillate perpendicular to each other and also to the direction of propagation. The Electromagnetic Wave is shown in a following diagram. The wave is propagating in ‘x’ direction. The electric field is varying in x-y plane. It is shown in red color. The magnetic field varies in x-z plane. It is shown in blue color. Crest (peak), trough, amplitude and wavelength are also shown in the diagram. Waves have two important characteristics - wavelength and frequency. The speed of light in a vacuum is a universal constant, about 300,000 km/s or 186,000 miles per second. The exact speed of light is: 299,792.458 km/s .It takes approximately 8.3 min for light from the sun the reach the earth (150,000,000 / 300,000 / 60 = 8.3) Taking the distance of the sun from Earth into account, which is 150,000,000 km, and the fact that light travels at 300,000 km/s, it shows in some way how fast light actually travels. Huygen put forth the theory of secondary wavelets. On its basis he developed the laws of reflections and refraction successfully. Later Young with his famous double slit experiment proved that the light waves interfere with each other. Only wave theory was able to explain the results of interference experiments. The phenomenon like diffraction and polarization were explained on the basis of wave theory. Hence wave nature of light was accepted widely. Newton’s corpuscular theory was not able to explain the interference, especially the dark bands. Diffraction and polarization were also not explained by corpuscular theory. Hence in the beginning of twentieth century Newton’s corpuscular theory of light was totally rejected. Photon Model of Light: In 1900 Max Planck proposed the existence of a light quantum, a finite packet of energy. Its energy depends on the frequency. This quantum of energy behaves like a particle. In 1905 Albert Einstein had proposed a solution to the problem of nature of light. He proposed behaviour of light having characteristics of both wave and particle theory. Einstein suggested that light is composed of tiny particles called photons, and each photon has energy. The light is emitted and absorbed as photons. It behaves as photons on micro-scale but it travels as wave. As a result of quantum mechanics, the dual nature of light is accepted. It is not a contradiction. The energy of each quantum is given by Max Plank’s equation E = hν = h (c/λ) where h is Planks constant. h = 6.34 x 10-34 J-s. Ray of light: Let us understand how light is represented when it is emitted from a source. Let the source be represented by a point source. We have already seen that when the dimensions of the object are small in given context, then the object is represented as the point object. e.g. i) city is represented as a point in the map of a nation ii) sun is represented as a point in galaxy. Let the given point source be placed in homogeneous medium like air or vacuum. Then the velociy of light will be same in all directions around the point source. Light originated from a point source will spread with same velocity in all directions. Light will travel equal distance in all directions in definite amount of time. The nature of the surface generated will be ‘spherical’. As the time goes on the radius of the surface will go on increasing. It is shown in the first diagram. We have already seen that ‘light travels in the form of waves. So we say, ‘a spherical wave is emitted from a point souce’. The spherical surface is called a ‘spherical wavefront’. The direction in which the wavefront spreads is along the radius of the sphere. They are called as the ‘rays’. Rays represent the direction of propagation of light. Such rays are shown in first and second diagram. The rays are perpendicular to the wavefronts. Let us understand the third and fourth diagram. We see sun from earth. The distance between sun and earth is 150, 000,000 km. The dimensions of the earth are very small and dimensions of a man are negligible. If a man looks towards the wavefront originated from sun and approaching towards him, then he is unable to detect the ‘curvature of the wavefront’. So it is called as the ‘plane wavefront.’ Hence all the wavefronts coming from the sources at practically infinite distances are considered as ‘plane wavefronts’. This is shown in the third and fourth diagram. We have already seen that the rays are perpendicular to the wavefront. The rays that represent the plane wavefront are parallel to each other. Conversely, if the rays are parallel then the wavefront is plane and source is assumed to be at infinity. http://www.physics.buffalo.edu/claw/Page18/ProjectCLAW-P18.html Ray representation of light is essential. Understanding of reflection, refractions, formation of images becomes easy using rays. Rectilinear Propagation of Light: Rectilinear Propagation of Light is the tendency of light to travel in straight Lines. Two beams of light if cross each other, they continue to travel as if the other were not present. Activity 1: Take two torches. Hold them in two hands parallel in front of a wall and make them on. The wall is white in color. We see two circular spots on the wall. Now turn your hands inwards. The circular spots start becoming oval. They approach towards each other. At one position they will superimpose on each other. Observe and note the intensity in this area. Continue turning of the torches. Now light spot on wall on your left is due torch in right hand and spot on your right side is due to torch in your left hand. They are at same level. The two beams will cross each other. Observe the intensities of light spots on the wall. What do you conclude? Do you agree with the above statement or not? Activity 2: Now wrap the heads of two torches one by red gelatin paper and other with green gelatin paper. Take red torch in left hand and green torch in the right hand. Repeat the steps of activity 1 sequentially. Which are the colors on your left and on your right on the wall after step 1? Which is the color of the spot after following step 2? Which are the colors on your left and right? What do you conclude? Do you agree with the above statement or not? In a homogenous transparent medium light travels in a straight line and this is known as rectilinear propagation of light. This can be demonstrated by the following experiment: Take three cardboards A, B and C and make a pinhole at their centers. Place a lighted candle on one side of the cardboard A and arrange the cardboards in such a way that the three pinholes and the candle flame are in a straight line. The candle flame will be visible through the pinhole of the cardboard C. Now slightly displace any one of the cardboards and try to see the flame through the pinhole of the cardboard C. The flame will not be visible. From this it is clear that light travels in a straight line. www.youtube.com/watch?v=2JnM3ezLdjE Effects of Rectilinear Propagation of Light: Light starting from any source travels in straight line. When there is opaque obstacle in its path, its shadow is formed. Here are some beautiful pictures of shadows. See the following pictures and imagine the position of the light sources. Umbra and Penumbra: Shadow is formed when light falls on an opaque obstacle. If the dimensions of the source are larger than the obstacle we get a complex shadow. In such shadow one region is completely dark and other is partially dark. If the source is too large w.r. to object then we do not get the shadow. Umbra region: The region where light from the source is totally blocked appears completely dark. Such region is called as the umbra region. Penumbra region: The region in which only a portion of the light from the source is reached is called as the penumbra region. The darkness of the penumbra is less than the umbra, and the brightness of penumbra is less than region of direct light. Thus, ‘Penumbra is a grey region.’ In first diagram the penumbra region is shown with constant shadow density. Actually this is not true. The penumbra shadow has a gradient of light. In following case the source is too large w. r. to object. There is no shadow at all. Activity3: Take a small torch and a tennis ball. The diameter of the torch should be less than the diameter of the ball. Hold the ball in left hand and torch in the right hand. Hold the ball about 25 cm from the wall and battery about 20-25 cm away from the ball. Put on the torch and observe the shadow. You will see a bigger umbra shadow of the ball. Take the torch nearer the ball and observe the shadow. Take the torch away from the ball and observe the shadow. Note your observations. Assignment 1: In above activity keep the distance of the ball 25 cm fixed from the screen. Keep the torch at 20 cm from the ball. Put it on. Measure the shadow of the ball. Repeat step two for distances of torch 15 cm and 25 cm. Take a proper scale and draw three ray diagrams. Formation of Eclipse An eclipse is an astronomical event. It is said to exist when an astronomical object is temporarily hidden or not seen because it passes through the shadow of another body. Alternatively if another body passes between it and the viewer, then it is called as an eclipse. The term eclipse is most often used to describe either a solar eclipse or a lunar eclipse. However, it can also refer to such events beyond the Earth-Moon system. Similar situation can take place for any other planet (in place of earth) and moon of that planet. It will also be called as the eclipse on that planet. http://www.youtube.com/watch?v=Qm4ZFyF8vmc Lunar eclipse: When moon passes through the shadow of the Earth, then the moon is not seen. This can happen only when the Sun, Earth, and Moon are aligned exactly in one line. Such event is called as the total lunar eclipse. However some light bends from the edges of the earth. It reaches the moon. We can see the moon as a very faint object. The lunar eclipse takes place on the full moon day. Sun is very large w. r. to earth and earth is very large w. r. to moon. Hence moon takes sufficiently long time while it passes through the umbra region of the earth. This is seen in the diagram below. The time of passage through the umbra is up to 107 minutes. The speed of the moon is nearly 1km/s. The time when moon touches penumbra region on one side and leaves the penumbra from other side is much larger. It is about four hours. This is also clear from the diagram below. Still, the eclipses are not seen on every full moon day. This is because the earth revolves around the sun in a definite orbit. Moon also revolves around the earth in orbit. The plane of the orbit of moon tilts w. r. to plane of orbit of Earth around Sun. The maximum angle between the planes of the two orbits is 50. It is seen in the second diagram. If one visualizes this, one can understand how the partial eclipse takes place. Lunar eclipse may be viewed from anywhere on the night side of the Earth. This is also clear from the above diagram. We will see ahead that solar eclipse can only be viewed from a certain relatively small area of the earth. This is because moon is much smaller than the earth. Lunar eclipses are safe to view without any eye protection or special precautions, as the moon is not brighter (indeed dimmer) than the full moon itself. Solar eclipse: When moon passes between Sun and Earth, then it partially or fully blocks the sun. This can happen only when the Sun, Moon and Earth are aligned exactly in one line. Such event is called as the solar eclipse. This can happen only at new moon day. However, total solar eclipses are rare at particular location. Moon is very small w. r. to earth and very very small w.r.to sun. The umbra region of the moon’s shadow on earth is on a small region. Total solar eclipse exists for a short time and in umbra region. The above two diagrams explain that the umbra region of the shadow of the moon is realy a small region. The sun is very large but very far, 500 light-second away from earth. Moon is comparatively small but it is much nearer, 1.2 l-s away from the earth. The ‘sun disc’ and ‘moon disc’ make approximately same angle with the eye. It is slightly more than half a arcminute or 32 arcseconds. Therefore we see size of the moon and size of the sun are same in the sky. However, the orbit of moon around the earth is not perfectly circle. It is elliptical. When moon is neared to earth, it appears big. When moon is away from the earth, it appears compartively small. When moon is nearer and bigger, and conditions of eclipse are attained; it covers the sun disc totally. This makes total solar eclipse. Conversly, when moon is farther and smaller, and conditions of eclipse are attained; it does not cover the sun disc totally. This makes annular solar eclipse. There are four types of solar eclipses: A total eclipse occurs when the Moon completely obstructs the intensely bright light of the Sun. There exists much fainter light due to solar corona. The totality occurs at best only in a narrow track on the surface of Earth. An annular eclipse occurs when the Sun and Moon are exactly in line, but the apparent size of the Moon is smaller than that of the size of the Sun. Hence the Sun appears as a very bright ring, or annulus, surrounding the dark disk of the Moon. A hybrid eclipse (also called annular/total eclipse) shifts between a total and annular eclipse. At certain points on the surface of Earth it appears as a total eclipse, whereas at other points it appears as annular. Hybrid eclipses are comparatively rare. A partial eclipse occurs when the Sun and Moon are not exactly in line. Moon partially obstructs the Sun. This phenomenon can usually be seen from a large part of Earth outside of the track of an annular or total eclipse. However, some eclipses can only be seen as a partial eclipse, because the umbra passes above the Earth's Polar Regions and never intersects Earth's surface. Above schematic diagram clearly explains the three situations. In first case, region A is the umbra region of the shadow of the moon. It is the situation of total solar eclipse. In the second situation, the umbra region of the shadow is finished early. Light from the periferi of sun, reaches to the ‘B’ region. Thefore, in B region it appears the annular solar eclipse. If it is seen from the penumbra region, it appears partial solar eclipse. Photograph of total solar eclipse: Following is the photograph of the total solar eclipse. When total solar seen with proper protection, we see the corona of the sun. We can also see solar flares. When moon starts shifting, sun starts appearing from one point. This point appears very bright. The situation is often reffered as the ‘diamond ring’ in the sky. Above two photograph are the photographs of annular solar eclipse. In first photograph, Moon covers the sun from the North- East corner. It forms the annular eclipse for a very short time. Then the moon leaves from south-west corner. Second photograph the only situation of the annular ring of solar eclipse. Precautions: It is dangerous to look directly at the Sun. It may burn the retina creating the permanent damage. Observers should use special eye protection or indirect viewing techniques while viewing a partial eclipse, or the partial phases of a total eclipse. It is safe to view the total phase of a total solar eclipse with the unaided eye and without protection. But such phase exists for a short time. In following two photographs, the first one is specially made ‘eclipse glasses’. Such specially made glasses remove the harmful part of Sun’s radiation. Sunglasses do not make viewing eclipse safe. Eclipse glasses Pinhole projection method of observing partial solar eclipse. http://www.bbc.co.uk/news/world-asia-22480509 Light Reflection from a Plane Surface: Plane has two dimensions only. This is a mathematical definition. We make certain surface plane by polishing it. Polishing is always done with the help of polishing paper or polishing material. Emery powder is generally used for polishing glass. We call certain surface a smooth surface when irregularities are undetectable. e.g. Wooden surface is tested by touch and said as smooth or rough. Certain surfaces are chemically treated to polish it. Still the irregularities remain on the atomic and molecular scale. They can be seen by using electron microscope. Optically plane surface: A certain surface is said to be optically plane provided the irregularities in the surface are less than the one tenth of the visible wavelengths. We have seen the range of the visible light is 380 nm to 780nm. Hence if the irregularities are of the order of 40 nm (or 480 AU or 480 x 10-10m), then such surface is called as the ‘optically plane’ surface. (The irregularity is having dimension th to th of the smallest wavelength). Whenever we say plane surface in optics, we mean it is optically plane. Regular reflection: The reflection of light from the plane surface is called as the regular reflection. In regular reflection the rays follow the laws of reflection. Irregular reflection or Scattering: The light reflected from rough surface or from the surface which is not optically flat is said to be scattered. The scattered light does not obey the laws of reflection. http://demonstrations.wolfram.com/ReflectionAndRefractionOnAFlatSurfaceBetweenTwoDifferentMat e/ http://zonalandeducation.com/mstm/physics/light/rayOptics/reflection/reflection1.html Regular reflection: When a ray of light strikes a plane mirror, the light ray reflects from the mirror. Reflection involves a change in direction of the light ray. The convention used to express the direction is in terms of the angle. These angles are the angles made with a normal line drawn at the point of incidence to the surface of the mirror. The angle of incidence is the angle between the normal line and the incident ray. The angle of reflection is the angle between the normal line and the reflected ray. Try to understand the following diagrams carefully. A three dimensional view of a single incident ray being reflected at the same angle off a plane (flat) mirror surface. Generally the laws of reflection are stated more explicitly as follows: First law of reflection: The angle of incidence is equal to the angle of reflection. i=r Second law of reflection: The incident ray and reflected rays are on both sides of a normal. Third law of reflection: The incident ray, reflected ray and the normal exist in one plane. We see all these three laws appear natural as we study the first diagram. We need to do an activity to get better understanding about third law. We shall see it. The second diagram is more realistic. We do not have a sharp pencil of ray every time. We have a beam of light. A beam of light is constituted of a set of rays. Whenever such set of rays is incident on a regular surface, each ray follows the laws of reflection separately. It appears that the beam of light also follows the laws of reflection. Activity 4: Obtain a ruby laser from the local market. Now a days they are available in general stores for key chains etc. They work on one or two 3A pencil cells. 3A pencil cells are smallest in size. Ruby lasers are available for ₹ 25 to ₹ 50 only. Take a protractor. Take a small wooden strip of size 2 to 2.5 cm in width, 4 to 5mm in thickness. The length should be equal to length of the protractor. It is available in the local market by name ‘lipping patti’. It is available in shops of plywood. Stick the protractor to wooden strip so that it stands vertically. Obtain a small plane mirror. Keep it horizontal on the table. Keep the protractor on the mirror. Shine the laser on the mirror such that it just touches the protractor. The situation is shown in the following diagram. (If you find this is difficult then keep the protractor horizontal and mirror vertical. It is easy to do. Then you can keep the laser on the table itself. Got it?) Observe the incident ray and reflected ray. Do they follow second law or not? Measure the angle of incidence from the normal. In the following picture it is 150. Similarly measure the angle of reflection. Compare them. Do they follow the first law or not? Turn the plane of the protractor. Move the laser also by hand. You will find that you are following the third law of reflection. Show and explain it to your friend. Your understanding will become better and he will also get inspired. Multiple Reflections: Image formation in plane mirror: Let us revise ourselves how we draw ray diagrams. We will understand it w. r. to following diagram. Here object is in front of the mirror and its image is formed in plane mirror. True ray diagram is w. r. to position of the eye. There are practically infinite rays starting from the point source. We consider only two rays starting from ‘a given point’. They strike the plane mirror and they are reflected by following laws of reflection. These rays enter our eye. They appear to come from a point. This point is located by extending the rays (which enter in the eye) behind the plane mirror. These extended rays are shown by dotted lines. Hence there is point image of every point on the object. These images finally form/construct total image of the object. Properties of the image formed in plane mirror. i) ii) iii) The size of the image is same as the size of the object. Image distance = object distance. There is lateral inversion. i.e. the left side of the object is right side of the image. Hence the image of ‘a b c d e f’ is laterally inverted in order ‘f e d c b a’. It is seen in the above diagram. Activity 5: Normally there is wall clock in every home. Hold a mirror near the wall clock. Observe the image of the clock. Enjoy how funny it looks. Take a white paper and sketch the image you see in the mirror. You will not forget the lateral inversion now. Multiple Mirror Systems Consider a system of two plane mirrors. They are placed together such that they have one edge common. They are as if hinged together, or let us hinge them for experiment. We get one image in each plane mirror. If we keep them at right angle then we get three images. If the angle between two mirrors is kept 600 then we get five images. One observes that as the angle between the mirrors decreases, the number of images that can be seen increases. In fact as the angle between the mirrors approaches 0 degrees (i.e., the mirrors are parallel to each other), the number of images approaches infinity. If we make a table of angle between mirrors and number of images formed, we find they obey an equation. Let the angle between two mirrors be noted by θ. The equation is stated as follows. –1 Hence when the angle is 900, the number of images is 3. For angle 600, the number of images is 5, and so on. If the angles are such that images are not in integer numbers, then we see full images of the nearest number. Activity 6: Take two small plane mirrors, say 15 cm x 10 cm (or even of smaller size). Place the polished surfaces face to face. Paste the cello tape on the back to back along the edge. Now the mirrors can be opened and folded. Make the angle 900, and let the mirrors stand side by side with each other. Place an object between the two mirrors. See 2, 3, 4, 5 images of the object. Measure the corresponding angle. Tabulate your result. Do your results fit in above formula? Consider a case when the mirrors are at right angles to each other. Generation of two images is not difficult to understand and explain. Each of the two mirrors produces an image due to the single reflection of light. The remaining image is produced as the result of multiple reflections of light. For third image the ray reflects once from each mirror. Right angle mirrors will allow maximum two reflections of light from the object. Assignment 2: Take two mirrors. Keep them at right angles. Place an object. See the three images. Take a paper. Draw two mirrors on this paper. Draw an object between the mirrors. Fix the position of the eye. Draw ‘eye’ at that position. Now construct the ray diagram. For the two images in two mirrors, you need to use single reflection for the ray entering in your eye. You need to use at least two reflections for a ray starting from the ‘third image’. Understand this properly. You will really enjoy this by drawing another diagram by changing the position of the eye. You need not change the position of the object. Or, you may keep the position of eye fixed and change the position of the object. Still the diagram is totally new though the angle between mirrors is same. Learn the side diagram. In first case the mirrors are at right angles. A ray is starting from the object. A ray returning after two reflections is antiparallel to the original ray. This is interesting. As the angle between the two mirrors decreases, three, four, and even more reflections can occur. Activity 7: Take two mirrors. Keep them at right angles. Keep the object away from the centers of the mirror. Draw an incident ray at some angle. Follow the laws of reflections and draw the reflected ray. It will definitely be incident on another mirror. Follow the laws of reflection and draw the second reflected ray. How is it? Is it antiparallel to incident ray or not? Activity 8: Take a paper. Draw two mirrors making angles 500. Draw an object between two mirrors. Draw an incident ray. Go on following the laws of reflection. See that the ray undergoes three reflections as seen in second diagram. Locating the images is comparatively simple. We can use the principle that image distance is equal to the object distance. The actual ray diagram is fairly complicated. Consider a case in which the mirrors make angle 600 between them. The images are shown. Try to understand how they are formed. Assignment: Write your explanation how the images are formed. Discuss it with your friends and teacher. See that your explanation is correct with physics point of view. (Note: virtual ‘objects’ do not exist.) A Pair of Parallel Mirrors When the two mirrors are aligned at a 0-degree angle with each other (i.e., a parallel mirror system), there are infinite number of images. Each image is the result of an image of an image, or an image of an image of an image or an image of an image of ... . The diagram below shows the multiple images for a parallel mirror system. http://www.youtube.com/watch?v=GKRwInEHsWc http://www.tutorvista.com/content/science/science-ii/reflection-light/multiple-choice.php 10) Spherical Mirrors Concave & convex mirrors Convergence & divergence of light Reflection of light from spherical mirrors Uses of mirrors Spherical Mirrors: We have seen the reflection and image formations from the plane mirrors up till now. Mirrors can also have regular curved shapes. Consider a glass sphere of radius 20 cm and wall thickness of 2 or 3 mm. If we take a vertical section as shown we get a spherical surface. Such surfaces are polished from both sides and silver coating is applied one side. This makes the spherical mirror. The silver coating is generally shown by the dashed shading. There are two types of mirrors, concave and convex. Concave mirror: When silver coating is on outer bulging side and inner side is reflecting, then the mirror is called as the concave mirror. Convex mirror: When silver coating is from inside and outer bulging side is reflecting, then the mirror is called as the convex mirror. We must get acquainted with few terms associated with the spherical mirrors. Pole: The geometrical center of the mirror is called as the pole of the mirror. It is generally denoted by ‘p’. Center of curvature: Every sphere has a center. This is the center of curvature of the mirror. Generally it is denoted by ‘c’. Principal axis: The line joining p and c is the radius of the sphere. It is perpendicular to the mirror at p. The line pc which is extended further is called as the ‘principal axis’ of the mirror. Radius of curvature: The distance pc is the radius of the sphere. It is called as the ‘radius of curvature of the mirror. Generally it is denoted by ‘R’. If the object is at infinite distance or practically at infinite distance then the rays coming from such object or source of light are parallel to each other. Activity: Take a small mirror of diameter of about 5cm. Also take a piece of paper. Hold a mirror in sunlight such that sunlight is incident on its reflecting surface. Take the paper in other hand hold it in front of the mirror. Move the paper too and fro. You will see a bright spot. Take the paper away, and try to explain what it is. Sun is very far, about 500 light-seconds away from earth. Rays coming from the sun are parallel to the principal axis. They are reflected from the mirror. They get concentrated at a point after reflection. This point is called as the ‘principal focus’ of the mirror. It is also called as the ‘focal point’ of the mirror. It is denoted by ‘F’. The focal point of a concave mirror is in front of the mirror while the focal point of the convex mirror is on the back side of the reflecting surface. It is shown in the following diagrams. The focal point is half way between pole and the center of the curvature. Focal length: The distance between pole (p) and principle focus (f) is called as ‘focal length’ of the mirror. It is denoted by ‘f’. Therefore the relation between radius of curvature and the focal length is R = 2f We know that the light rays retrace their paths. Hence if the source of light is kept at the focus of the mirror on principal axis then the rays will travel parallel to the principal axis after reflection. Convergence & divergence of light Convergence: We have seen the phenomenon that a set of parallel rays get reflected from the concave mirror. Each ray follows the laws of reflection at the point of incidence. These rays pass through the focus. This phenomenon is called as convergence. The rays are said to converge after reflection. Therefore the concave mirror is also converging mirror. See the diagram above. Following diagrams represent the relation between wavefront and rays. We have the ray representation and wave representation. Consider a situation where a set of parallel rays is incident on concave mirror. It means a wavetrain of plane wavefronts is incident on the concave surface. The reflecting wavefront will be converging spherical wavefront. Similarly consider a situation in which a plane wavefront is incident on the convex mirror. The reflecting wavefront will be diverging wavefront. You can observe this in animation in the link given below. http://www.physics.uq.edu.au/people/mcintyre/vergences/optics/go_mirr.html Activity: Observe the animation in the above link carefully. i) Construct a diagram in which a plane wavefront is incident on the concave mirror. Draw a set of reflected waves carefully. ii) Repeat the exercise for the convex mirror also. Assignment: If you neatly observe then the ‘curvature’ of the reflected wavefront is more than the curvature of the mirror. Construct your explanation for it. Discuss it with your teacher. Reflection of light from spherical mirrors: Image formation of spherical mirror We have seen reflection of light by plane mirrors. Now we will understand the reflection of light by spherical mirrors. When an object is placed in front of any mirror, light rays from the object fall on mirror and get reflected. The reflected rays produce an image, where they intersect or appear to intersect. This image formation is normally shown by the ray diagram. While drawing the ray diagrams, we have to follow some rules. The rules are as follows: An incident ray parallel to principle axis after reflection from spherical mirror passes through its focus. An incident ray passing through focus emerges parallel to principal axis after reflection. An incident ray passing through center of curvature of a concave mirror retraces its path after reflection. Assignment 1: Why does the ray passing through the center of curvature of spherical mirror retraces its path? Image formation by concave mirror: The rays of an object at practically infinity are almost parallel to each other. Let us consider such two rays are incident on mirror. One ray strikes at its pole and other is passing through the center of curvature. In case of ray incident on pole, AP is incident ray and PB is reflected ray. The angle of incidence APC is equal to angle of reflection CPB. The second ray CQ retraces its path after reflection as it is passing through center of curvature. These reflected rays intersect each other at ‘I’ and an image is formed. This point is known as focus of the lens. The image formed is real, inverted and diminished. This is shown in the following diagram. Here, we have seen the image formation of an object at infinity. For an object at various positions, go through the following link. Image formation by concave mirror.pptx Image formation by convex mirror: Let us see the, images produced due to reflection of light from convex mirror. 1) An object is in between infinity and pole: The ray diagram for this is as follows. The image is formed between focus and pole. Image is virtual and diminished. Assignment 2: Draw a ray diagram of an image formation, when an object is at infinity. Uses of mirrors We use the plane mirrors daily for seeing whether we are well dressed or not. Small plane mirrors are used to construct huge concave and parabolic solar energy concentrators. They are also used in construction of perimeters. Convex mirrors are used as rear view mirrors in every vehicle. The mirror is near the driver or on both sides of a vehicle. Concave mirror with long focal lengths can be used as makeup mirror, shaving mirror or a dentist's mirror as they form magnified and upright image Concave mirrors are used when we want to see the details of the face. They are used for make-up. Dentists also use the small concave mirrors to see the damaged teeth. They are used in head lights of vehicles. Headlights mirrors are parabolic now days. Concave mirrors are used in reflecting telescopes. The study of mirrors will continue with image formation by spherical mirrors. There we will learn various related formulae. It will help us in the design of various optical instruments.