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| Summary (Contd…) |
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 Two main types of spectra are: |
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| - Emission spectrum |
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| - Absorption spectrum |
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The emission spectrum is further of three types: |
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| - Continuous emission spectrum, which contains all the wavelengths in a particular region. The range of wavelengths emitted depends only on temperature of the source. |
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| - Line emission spectrum consists of a few bright lines on a dark background. Each line corresponds to a particular wavelength. It is an atomic spectrum emitted by elements heated to suitable temperatures. Every element has its own characteristic line emission spectrum. |
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| - Band emission spectrum consists of a few bright patches of light over a dark background. Each bright patch is called a band. Band emission spectrum is a molecular spectrum emitted by compounds when heated to suitable temperature. |
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| - Absorption spectrum of a substance consists of wavelengths or groups of wavelengths absorbed by the substance when continuous light is passed through the vapors of the substance. The wavelengths absorbed appear as dark lines or bands on a bright background. |
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According to Kirchhoff's law an element can absorb only those wavelengths from continuous light, which it emits at the same temperature. This law was used to study structure of the Sun when Fraunhoffer explained existence of some dark lines called Fraunhoffer lines in the observed spectrum of the Sun. When continuous light from the central core (photosphere) of the Sun passes through chromo- sphere, outer part of Sun, vapors of elements present in chromosphere absorb certain wavelengths. These wavelengths are missing in the spectrum of the sun. The dark lines corresponding to the missing wavelengths are the Fraunhoffer lines. The elements in chromosphere, identified based on Kirchhoff's law were hydrogen, sodium, iron, calcium etc. |
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The blue colour of the sky is due to scattering of Sunlight from molecules of earths atmosphere. |
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| As lb
< lr and intensity of scattered light
varies inversely as fourth power or wavelength, therefore, maximum scattering is of blue colour. |
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| At the time of sunrise and sunset, light from Sun has to pass maximum distance through Earth's atmosphere. |
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| As lr
> lb red color is scattered least and
can enter into our eyes. That is why sun looks red at the time of sunrise and sunset. Clouds are seen due to scattering of light from lower parts of atmosphere, which contains large dust particles. All colors are scattered equally. Hence, clouds look white. |
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A rainbow is a spectrum of sunlight seen through raindrops suspended in air. It is seen in the sky usually after rain when the back of the observer is towards the sun. |
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| Primary rainbow is much brighter with inner edge violet and outer edge red, subtending 410-430 angle on observer's eye. |
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| Secondary rainbow is fainter with inner edged red and outer edge violet, subtending an angle 510 - 540 from an observer's eye. |
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A simple microscope is used for observing magnified images of tiny objects. |
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| It consists of a converging lens of small focal length. Object is held between principal focus and optical centre of the lens. The image formed is virtual, erect and magnified. |
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| Magnifying power of a simple microscope is defined as the ratio of the angles subtended by the image and the object on the eye, when both are situated at the least distance of distinct vision (D) from the eye. |
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Magnifying power is given by  |
| In a compound microscope, the images are highly magnified. The objective lens forms a real, inverted and magnified image of the object. This acts as an object for eye lens, which forms a virtual, erect and magnified image seen by the eye held close to the eye lens. Magnifying power of a compound microscope is given by |
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| Where u and v are distances of object and image from optical centre of objective lens, fe is focal length of eye lens. |
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An astronomical telescope is used for observing heavenly bodies like stars and planets etc. |
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| The objective lens forms a real, inverted and smaller image of distant object in its focal plane. This image serves as the object for eye lens, which forms a virtual, erect and magnified image seen by the eye held close to the eye lens. In normal adjustment, final image as seen by the eye is at infinity. In normal adjustment, magnifying power of astronomical telescope is given by |
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| When final image is at the least distance of distinct vision from the eye, the magnifying power is given by |
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In a terrestrial telescope, final image has to be made erect with respect to the object. |
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| For this, we have to use an erecting lens between objective lens and eye lens. Expressions for magnifying power remains the same. But the length of telescope tube increases by 4f, where f is the focal length of erecting lens. To overcome this difficulty, Gatile, a telescope is used, in which eye lens is concave. In normal adjustment, length of the tube becomes (fo - fe) but field of view is much smaller because of concave lens. |
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| In a reflecting telescope, the objective lens is replaced by a concave parabolic mirror. |
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| Magnifying power of a reflecting type telescope is |
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Wave optics is based on wave theory of light put forward by Huygen and modified later by Fresnel. According to the wave theory, light is a form of energy, which travels through a medium in the form of transverse waves. |
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A wavefront is defined as the locus of all the particles of a medium, which are vibrating in the same phase. When the source of light is a point source, the wave front is spherical. When source is linear, the wave front is cylindrical. At very large distances from the source, a portion of spherical or cylindrical wavefront appears to be plane. A wavefront travels parallel to itself and perpendicular to the rays. |
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Huygens's principle of geometrical construction of a wave front at any instant says : |
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| - Every point on a given wave front (called primary wave front) acts as a source of new disturbance called secondary wavelets. |
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| - The secondary wavelets travel in all directions with the speed of light in the medium. |
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| - A surface touching these secondary wavelets tangentially in forward direction at any instant gives the new (secondary) wave front at that instant. |
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| Using Huygenss principle, we can prove the laws of reflection and the laws of refraction on the basis of the wave theory. |
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Superposition principle says that when two or more wave motions traveling through a medium superimpose one another, they lose their individual identity. A new wave is formed in which resultant displacement (y) at any instant is equal to the vector sum of the displacements due to individual waves at that instant i.e., |
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| This principle applies to mechanical waves as well as electromagnetic waves. |
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Interference of light is the phenomenon of redistribution of light energy on account of superimposition of light waves from two coherent sources. At the points where resultant intensity is maximum, interference is said to be constructive. At the points where the resultant intensity is minimum, interference is said to be destructive. |
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| Thomas Young's double slit experiment was the first to demonstrate the phenomenon of interference of light. Using two slits illuminated by monochromatic light source, the obtained bright and dark bands of equal widths were placed alternately. These were called interference fringes. All bright fringes have the same intensity and all dark fringes are perfectly dark. |
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| If W1, W2 are widths of two slits; I1, I2, are intensities of light coming from these two slits : a, b are the amplitudes of light from these slits, then, |
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| The condition for constructive interference is that the path difference between two waves should be zero or an integral multiple of full wavelength. In that event, the crest of one wave would fall on the crest of the other and trough on the trough. |
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| The resultant amplitude = (a + b). |
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| The condition for destructive interference is that the path difference between two waves should be an odd integral multiple of half the wavelength. In the event, the crest of one wave would fall on the trough of the other and vice versa. The resultant amplitude = (a - b) |
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| Therefore, in the interference pattern, we have |
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 for nth bright fringe. |
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| Where n = 0 for central bright fringe. |
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| n = 1 for first bright fringe, n = 2 for second bright fringe and so on. |
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| Here x is distance of nth bright fringe from the centre. |
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| For nth dark fringe, |
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 |
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| Where n = 1 for first dark fringe |
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| n = 2 for 2nd dark fringe and so on. |
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The width of each (bright or dark) interference fringe is found to be  |
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| where D is the distance of the screen from the coherent sources and d is the distance between the two coherent sources. When a source gives white light, interference fringes are colored. Red fringes are wider as lr is large. Coherent sources are those, which emit continuous light waves of same amplitude, same wavelength/frequency in the same phase or having a constant phase difference. Two independent sources can never be coherent. Coherent sources are usually the object-image sources. i.e., they are produced from a single source of light. |
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| Coherent sources are an essential requirement for interference of light. |
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| They should be strong, with least background, lying close to each other. |
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Diffraction of light is the phenomenon of bending of light around corners of an obstacle or aperture in the path of light. On account of this, bending light penetrates into the geometrical shadow of an obstacle. The diffraction pattern due to a single slit consists of a central bright band, which has alternate dark and weak bright bands of decreasing intensity on both sides. |
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The condition for nth secondary minimum is that: |
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| path difference = a sin qn = n; where n = 1, 2, 3… and the condition for nth secondary maximum is that: |
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| path difference = a sin qn = (2n + 1) l/2 where n = 1, 2, 3… |
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| Here, a is the width of the slit and D is the distance of the screen from the slit. f is focal length of lens for diffracted light. |
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| Diffraction is supposed to be due interference of secondary wavelets from the exposed portion of wavefront from the slit, whereas in interference, all bright fringes have same intensity. In diffraction, bright bands are of decreasing intensity. |
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According to Doppler effect in light, whenever there is a relative motion between a source of light and an observer, the apparent frequency of light received by the observer is different from the frequency of light emitted from the source of light. The apparent frequency f1 is given by: |
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 |
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| where v is the velocity of the star and c is the velocity of light in vacuum. f is the actual frequency of light emitted from the source. |
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| + sign is used when the source moves towards the observer and vice-versa. We can show that |
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| when a star is approaching the earth f1 > f, Df is positive. Accordingly, |
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| f1 < f and Df is negative. |
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| The spectrum of the star shifts towards the violet end (lower wavelength side). Similarly when a star moves away from the Earth, the spectrum of the star shifts towards the red end, (higher wavelength side). Doppler effect in light is used in measuring speed of a star or galaxy, satellites, aero planes, submarines etc. |
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Polarization of light is the phenomenon of restricting the vibrations of light (electric vector) in a particular direction; on passing ordinary light (unpolarised) through certain crystals like tourmaline crystal. This crystal acts as a polarizer. The plane in which the vibrations of polarized light are confined is called the plane of vibration. A plane perpendicular to the plane of vibration is called the plane of polarization. |
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| One eye cannot detect whether light is polarized or not. To detect polarization, we have to use another crystal, which acts as the analyzer. When axes of polarizer T1 and analyzer T2 are parallel, the intensity and character of light transmitted by T1 and T2 remain unaffected. However, when axes of the two crystals are at 900 to each other, light is completely cut off. This establishes that light waves are transverse in character. |
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| When unpolarised light is seen through a single crystal (polaroid), intensity of transmitted light decreases on account of polarization. However, on rotating the crystal in the same direction of propagation as axis, intensity of polarized light does not change. |
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According to law of Malus, when a beam of completely plane polarized light is incident on an analyzer, the resultant intensity of light (I) transmitted from the analyzer varies directly as the square of the cosine of the angle (q) between plane of transmission of the analyzer and the polarizer. |
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| i.e., I a cos2q |
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According to Brewster's Law, when unpolarised light is incident at polarizing angle (ip) on an interface separating a rarer medium from a denser medium of refractive index m such that tan ip, then light reflected in the rarer medium is completely polarized. The reflected and refracted waves in this case are perpendicular to each other. Obviously polarizing angle depends on nature of media in contact and on the colour of light. |
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Main uses of
Polaroid are in wind shields of automobiles, sun glasses etc., They reduce head light glare of cars, improve colour contrast in old paintings, etc.. They are also used in three-dimensional motion pictures and in optical stress analysis. |
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