DIFFRACTION & POLARISATIONLS 14/AS 26TH,NOV,09 7.30P.M : DIFFRACTION & POLARISATIONLS 14/AS 26TH,NOV,09 7.30P.M DIFFRACTION DUE TO SINGLE SLIT..
POLARSITATION
BREWESTERS LAW
DIFFRACTION : DIFFRACTION DIFFRACTION OF LIGHT
Diffraction of light is the phenomenon of bending of light around corners of an obstacle or aperture in the path of light. 2
DIFFRACTION : DIFFRACTION On account of this bending, light penetrates into the geometrical shadow of the obstacle. 3
DIFFRACTION : DIFFRACTION The deviation becomes much more pronounced when the dimensions of the aperture or the obstacle are comparable to the wavelength of light. 4
DIFFRACTION IN SOUND : DIFFRACTION IN SOUND In case of sound waves and radio waves, diffraction is observed readily because wavelength of these waves is large, and obstacles/apertures of this size are readily available. 5
DIFFRACTION : DIFFRACTION For visible light, ? is very small
Therefore, diffraction of visible light is not so common, as obstacles/apertures of this size are hardly available. 6
DIFFRACTION : DIFFRACTION According to Fresnel, diffraction occurs on account of mutual interference of secondary wavelets starting from portions of the wave front which are not blocked by the obstacle or from portions of the wave front which are allowed to pass through the aperture. 7
FRESNEL : FRESNEL 8
DIFFRACTION OF LIGHT AT A SINGLE SLIT : DIFFRACTION OF LIGHT AT A SINGLE SLIT S is a monochromatic light source held at the focus of a collimating lens .
A parallel beam of light emerging from the lens with a plane wavefront is made to fall on a single slit AB. 9
DIFFRACTION AT A SINGLE SLIT : DIFFRACTION AT A SINGLE SLIT As width of slit AB = a is
of the order of wavelength of light, therefore, diffraction occurs on passing through the slit.
The diffraction pattern is focused on to the screen XY with the help of a convex lens 10
DIFFRACTION AT A SINGLE SLIT : DIFFRACTION AT A SINGLE SLIT The diffraction pattern obtained on the screen consists of a central bright band, having alternate dark and weak bright bands of decreasing intensity on both sides. 11
DIFFRACTION AT A SINGLE SLIT : DIFFRACTION AT A SINGLE SLIT Theory
The set of parallel rays falling on the slit form a plane wave front,
.According to Huygens principle, each point on the unblocked portion of plane wave front AB sends out secondary wavelets in all the directions. 12
DIFFRACTION : DIFFRACTION The secondary waves, from points equidistant from the centre C of the slit lying in the portion CA and CB of wave front travel the same distance in reaching O, and hence the path difference between them is zero. These secondary waves reinforce each other, resulting in the maximum intensity at point O. 13
DIFFRACTION AT A SINGLE SLIT : DIFFRACTION AT A SINGLE SLIT Positions of Secondary Minima
Consider the secondary waves travelling in a direction making an angle with CO.
All the secondary waves travelling in this direction reach a point P on the screen.
The intensity at P will depend on the path difference between the secondary waves emitted from the corresponding points of the wave front. 14
DIFFRACTION AT A SINGLE SLIT : DIFFRACTION AT A SINGLE SLIT Draw AN perpendicular to BK. Path difference between the secondary waves reaching P from A and B = BN = AB sin
= a sin 15
DIFFRACTION : DIFFRACTION CONDITION FOR MINIMA
If this path difference is ?, (the wavelength of light used), then P will be point of minimum intensity.
This is because the whole wave front can be considered to be divided into two equal halves CA and CB.
If the path difference between the secondary waves from A and B is ?, then the path difference between the secondary waves from A and C reaching P will be ?/2.
When both these half’s superimpose. A minima is created.
P is a point of First secondary minimum. 16
DIFFRACTION AT A SINGLE SLIT : DIFFRACTION AT A SINGLE SLIT In general, therefore, we have for nth secondary minimum
where gives the direction of the nth secondary minimum and n = 1,2,3….., an integer. 17
DIFFRACTION AT A SINGLE SLIT : DIFFRACTION AT A SINGLE SLIT 18
DIFFRACTION AT A SINGLE SLIT : DIFFRACTION AT A SINGLE SLIT Positions of Secondary Maxima
If any other point (not shown) is such that the path difference 19
DIFFRACTION AT A SINGLE SLIT : DIFFRACTION AT A SINGLE SLIT will be the position of first secondary maximum.
Here, we can imagine the unblocked wave front to be divided into three equal parts, so that the path difference between secondary waves from corresponding points in the 1st two parts will be ?/2.
The superposition of first two halves will give rise to destructive interference.
The secondary waves from the third part, however, remain unused and, therefore, they reinforce each other and produce first secondary maximum. 20
DIFFRACTION : DIFFRACTION In general, we have for nth secondary maximum. 21
DIFFRACTION : DIFFRACTION The DIFFRACTION PATTERN due to single slit consists of a central bright maximum at O along with secondary minima and maxima on either side. The intensity distribution on the screen is represented in Fig. 22
DIFFRACTION AT A SINGLE SLIT : DIFFRACTION AT A SINGLE SLIT The point O corresponds to the position of central bright maximum and the points with path difference, a sin ?= ? ,2?……. are secondary minima. The secondary maxima are the points in between secondary minima and are of rapidly decreasing intensity. 23
DIFFRACTION AT A SINGLE SLIT : DIFFRACTION AT A SINGLE SLIT Width of central maximum
The width of central maximum is the distance between first secondary minimum on either side of O. If P is the position of Ist secondary minimum and OP = x, then from (1) 24
DIFFRACTION AT A SINGLE SLIT : DIFFRACTION AT A SINGLE SLIT If f is focal length of lens which is held very close to the slit, then f = D = distance of the slit from the screen.
? is obviously half the angular width of central maximum of diffraction pattern of single slit. 25
DIFFRACTION AT A SINGLE SLIT : DIFFRACTION AT A SINGLE SLIT 26
Difference in diffraction pattern at single slit due to monochromatic light and white light. : Difference in diffraction pattern at single slit due to monochromatic light and white light. When source of light is monochromatic, the diffraction pattern consists of alternate bright and dark bands of unequal widths. The central bright fringe has maximum intensity. 27
Difference in diffraction pattern at single slit due to monochromatic light and white light. : Difference in diffraction pattern at single slit due to monochromatic light and white light. When source is emitting white light, the diffraction pattern is coloured. The central maximum is white, but other bands are coloured.
As band width ,therefore, red band with higher wavelength is wider than the violet band with smaller wavelength. 28
DIFFERENCE BETWEEN INTERFERENCE AND DIFFRACTION OF LIGHT : DIFFERENCE BETWEEN INTERFERENCE AND DIFFRACTION OF LIGHT .
INTERFERENCE 1. Interference is due to superposition of two distinct waves coming from two coherent sources. DIFFRACTION Diffraction is produced as a result of superposition of the secondary wavelets coming from different parts of the same wave front. 29
DIFFERENCE BETWEEN INTERFERENCE AND DIFFRACTION OF LIGHT : DIFFERENCE BETWEEN INTERFERENCE AND DIFFRACTION OF LIGHT INTERFERENCE 2. In interference pattern, all the bright fringes(or bands) are of same intensity. DIFFRACTION In diffraction pattern all the bright bands are not of the same intensity 30
DIFFERENCE BETWEEN INTERFERENCE AND DIFFRACTION OF LIGHT : DIFFERENCE BETWEEN INTERFERENCE AND DIFFRACTION OF LIGHT INTERFERENCE 3. In interference pattern, intensity of minima is generally zero or very small and there is a good contrast between bright and bark fringes. DIFFRACTION In diffraction pattern, the intensity at minima is never zero and there is poor contrast between bright and dark bands. 31
DIFFERENCE BETWEEN INTERFERENCE AND DIFFRACTION OF LIGHT : DIFFERENCE BETWEEN INTERFERENCE AND DIFFRACTION OF LIGHT INTERFERENCE The width of the interference fringes may or may not be equal. DIFFRACTION But the width of diffraction bands is always unequal. 32
FRESNEL DISTANCE : FRESNEL DISTANCE Fresnel distance is the minimum distance a beam of light has to travel before its deviation from straight line path becomes significant. 33
POLARIZATION OF LIGHT : POLARIZATION OF LIGHT Light is an electromagnetic wave in which electric and magnetic field vectors vary sinusoid ally
perpendicular to each other as well as perpendicular to the direction of propagation of wave
POLARIZATION OF LIGHT : POLARIZATION OF LIGHT Symbol of unpolarised light is shown in fig. 35
POLARIZATION OF LIGHT : POLARIZATION OF LIGHT This phenomenon of restricting the vibrations of light (electric vector) in a particular direction, perpendicular to the direction of wave motion is called polarization of light.
The tourmaline crystal acts as a polarizer.
POLARIZATION OF LIGHT : POLARIZATION OF LIGHT Thus electromagnetic waves are said to be polarized when their electric field vectors are all in a single plane, called the plane of oscillation or vibration.(ABCD) 37
POLARIZATION OF LIGHT : POLARIZATION OF LIGHT The plane ABCD in which the vibrations of polarized light are confined is called the plane of vibration. The plane KLMN which is perpendicular to the plane of vibration is defined as the plane of polarization.
EXPERIMENTAL DEMONSTRATION OF POLARIZATION OF LIGHT : EXPERIMENTAL DEMONSTRATION OF POLARIZATION OF LIGHT Here T1 and T2 are two thin plates of tourmaline, cut with their faces parallel to the axis of crystal. A fine pencil of ordinary light from the source S is passed through the plate T1; and the light transmitted is observed by the naked eye.
EXPERIMENTAL DEMONSTRATION OF POLARIZATION OF LIGHT : EXPERIMENTAL DEMONSTRATION OF POLARIZATION OF LIGHT When the plate T1 is rotated the direction of propagation of light as axis, the intensity and character of transmitted light remain the same.
Let the second plate T2 be placed in the path of light transmitted from T1.
We observe that intensity and character of light transmitted by T1 and T2 remain unaffected only when T1 and T2 are set with their axes parallel. 40
EXPERIMENTAL DEMONSTRATION OF POLARIZATION OF LIGHT : EXPERIMENTAL DEMONSTRATION OF POLARIZATION OF LIGHT When T2 is rotated gradually, intensity of light transmitted from T2 goes on decreasing. As soon as the axes of the two crystals are at 90o to each other, light is completely cut off.
The phenomenon can be explained only when we assume that light waves are transverse.
NICOL PRISM : NICOL PRISM A nicol prism is an optical device, which is used for producing plane polarized light and analyzing the same.
NICOL PRISM : NICOL PRISM The nicol prism consists of two calcite crystals cut at = 68o with its principal axis joined by a glue called Canada balsam. The refractive index of this glue is 1.55. 43
NICOL PRISM : NICOL PRISM When a beam of unpolarised light is passed through a calcite crystal, it breaks up into two rays:
(I) Ordinary ray (O-ray), which has its electrical vector perpendicular to the principal section of the crystal.
(ii) Extraordinary ray (E-ray),which has it electric vector parallel to the principal section of the crystal. 44
NICOL PRISM : NICOL PRISM As refractive index of calcite for O-ray is 1.658, and for E-ray is 1.486, therefore,canada balsam(with ? = 1.55) acts as a rarer medium for O-ray and it acts as a denser medium for E-ray.
NICOL PRISM : NICOL PRISM Therefore, when O-ray passes from a portion of crystal into the layer of Canada balsam, it passes from a denser to a rarer medium. When angle of incidence is greater than the critical angle (ic =69o)
The O-ray is totally internally reflected and is not transmitted. The E-ray is not affected and is transmitted as such through the nicol prism.
This is how unpolarized light passed through a nicol prism becomes plane polarized.
DETECTION OF POLARIZED LIGHT : DETECTION OF POLARIZED LIGHT A naked eye cannot distinguish between polarized and unpolarized light. A calcite crystal, quartz crystal, a nicol prism(made from calcite crystal) can be used as polarizer as well as analyzer of polarized light.
When unpolarized light is seen through a single crystal (Polaroid) intensity of transmitted light decreases, on account of polarization. On rotating the crystal, intensity of polarized light does not change.
DETECTION OF POLARIZED LIGHT : DETECTION OF POLARIZED LIGHT However, when light transmitted from Polaroid P, is seen through another Polaroid P2 and P2is rotated, the transmitted fraction of light from P2 falls from maximum to zero as the angle between P1 and P2 varies from 0o to 90o respectively. Here, P1 is called polarizer and P2 is called analyzer.
LAW OF MALUS : LAW OF MALUS 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 (?) between plane of transmission of analyzer and polarizer.
LAW OF MALUS : LAW OF MALUS When polarizer and analyzer are perpendicular to each other,
POLARIZATION BY SCATTERING : POLARIZATION BY SCATTERING When a beam of white light is passed through a medium containing particles whose size is of the order of wavelength of light, then the beam gets scattered. When the scattered light is seen in a direction perpendicular to the direction of incidence, it is found to be plane polarized.
POLARIZATION OF LIGHT BY REFLECTION : POLARIZATION OF LIGHT BY REFLECTION When unpolarized light is reflected from a surface, the reflected light may be completely polarized, partially polarized or unpolarized. This would depend on the angle of incidence.
POLARIZATION OF LIGHT BY REFLECTION : POLARIZATION OF LIGHT BY REFLECTION If angle of incidence is 0o or 90o,the reflected beam remains unpolarized. For angles of incidence between 0o or 90o, the reflected beam is polarized to varying degree. 53
POLARIZATION OF LIGHT BY REFLECTION : POLARIZATION OF LIGHT BY REFLECTION The angle of incidence at which the reflected light is completely plane polarized is called polarizing angle or Brewster’s angle. It is represented by ip. 54
POLARIZATION OF LIGHT BY REFLECTION : POLARIZATION OF LIGHT BY REFLECTION The reflected light therefore, contains vibrations of electric vector perpendicular to the plane of incidence. Hence the reflected light is completely plane polarized in a direction perpendicular to the plane of incidence.
BREWSTER’S LAW : BREWSTER’S LAW According to this law, when unpolarized light is incident at polarizing angle, ip on an interface separating air from a medium of refractive index ?,then the reflected light is fully polarized(Perpendicular) to the plane of incidence). Provided
It has been observed experimentally that when light is incident at polarizing angle, the reflected component along OB and refracted component along OC are mutually perpendicular to each other.
: Thus, BREWSTER’S LAW
BREWSTER’S LAW : BREWSTER’S LAW .
BREWSTER’S LAW : BREWSTER’S LAW Using Brewster’s law, we can calculate polarizing angle for any two media in contact. For example.
POLAROIDS : POLAROIDS A Polaroid is a material which polarizes light. Tourmaline is a natural polarizing material. Polaroid's are now artificially made. It was discovered that small needle shaped crystals of quinine idosulphate have the property of polarizing the light. A number of these crystals with their axes parallel to one another are packed in between two parallel to one another are packed in between two sheets of plastic. Such a sheet serves as the Polaroid.
POLAROIDS : POLAROIDS Uses of Plane polarized light and Polaroid's
1. One of the major uses of Polaroid's is to avoid glare of light. When we use polarized sun glasses with their vibration plqanes-vertical,the most of the polarized light reflected from glazed surfaces is cut off.
POLAROIDS : POLAROIDS 2. To avoid the dazzling light of a car approaching from the opposite side during night driving, Polaroid's are fitted on the wind shield and on the cover glasses of head lights of each car. The arrangement is so made that Polaroid's on the wind shield on one car and those on cover glasses of head lights of other car become ‘crossed’.
POLAROIDS : POLAROIDS 3. The microscopes objectives are fitted with Polaroid's to avoids glare in observing very minute particles.
4. Clear photographs of white clouds are obtained by fitting Polaroid's in front of the camera lens. Scattered light present in the atmosphere, which is partially polarized is cut off by the Polaroid.
POLAROIDS : POLAROIDS 5.Polaroids are useful in three dimensional motion pictures,i.e. in holography.
6. In calculators and watches, letters and numbers are formed by liquid crystal display(LCD) through polarization of light.
7.In CD players, polarized laser beam acts as needle for producing sound from compact disc, which is in encoded digital format.
Slide 65 : For all your Physics Problems
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