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Transcript
Summary so far…. E y2 E0 y 2 1. 2 Ex2 E0 x 2 2 Ex Ey E0 x E0 y cos sin 2 (o ~ E )d 0,2 ,4 ,6 ,..... 2n or 0, ,3 ,5 ,..... (2n 1) The emergent ray will be linearly polarized light. 3 5 2. 2 , 2 , 2 ,..... (2n 1) 2 The emergent ray will be circularly polarized if is 450 otherwise elliptically polarized light. Note: ε=+ve for RCP or REP and ε=-ve for LCP or LEP RETARDERS Optical devices which introduce a phase difference between e- and orays. These are in the form of plates of doubly refracting crystal cut in such a way that optic axis is parallel to the refracting surfaces. ( E ~ o )d 4 i.e. 2 Quarter wave plate, produces linearly polarized light for incident plane pol light if =0 0r 900 (b/w optics axis and E-vector) ( E ~ o )d Quarter wave plate, circularly if =450 2 else elliptically polarized light i.e. produces HWP convert RCP or REP light to LCP or LEP and vice verse. PRODUCTION OF POLARIZED LIGHT 1. Plane polarized light: Un-polarized light Plane polarized light 2. Circularly polarized light: Un-polarized light Plane polarized light Vibration makes 450 angle with optic axis. 3. Elliptically polarized light: QWP Elliptically polarized Un-polarized light Plane polarized light Vibration makes angle other than 450. ANALYSIS OF POLARIZED LIGHT 1. Plane polarized light: If intensity varies from maxima to minima with zero during the full rotation of analyzer then light is plane polarized. 2. Circularly polarized light: No variation in - It may be a un intensity. polarized or - It may be a circularly polarized light If variation in intensity is like plane polarized light original light is circularly polarized. QWP Otherwise, original light is un-polarized. 3. Elliptically polarized light: Variation of intensity - It may be a partially from a maximum to polarized or minimum but not zero - It may be an elliptically polarized light If variation in intensity is like plane polarized light original light is circularly polarized. QWP Otherwise, original light is partially-polarized. Quest: What about superposition of two circularly polarized light (RCP and LCP) beams with same amplitude and wavelength. Any plane polarized light wave can be obtained as a superposition of a left circularly polarized and a right circularly polarized light wave, whose amplitude is identical. This is the base of Fresnel’s theory of optical rotation Try it mathematically too Optical activity The phenomenon of rotation of the plane of vibration is called rotatory polarization and this property of the crystal (substance) is called optical activity or optical rotation and substances which show this property are called optically active substances. optical activity : First time experimentally observed by Arago in 1811. I=0 Observation: In the absence of Quartz, I=0. Along optic axis Vo=Ve or μo = μe Or no phase or path diff along the optics axis Or no birefringence optical activity : First time experimentally observed by Arago in 1811. Two Crossed Nicol Observation: analyser polarizer I Quartz plate In the absence of Quartz, I=0. In the presence of quartz, I is not zero In quartz, when optic axis is perpendicular to refracting face, Plane pol. Light should pass without any change no birefringence, so I should be zero after analyzer. Presence of intensity shows the rotation of the plane pol light by the quartz material Conclusion: Plane polarized light is rotated because of quartz There are two types of optically active substances: • Righthanded or dextro-rotatory:Sodium chlorate, cane sugar. • Left handed or leavo rotatory:Fruit sugar, turpentine. Note: Quartz is an optically active substance. Calcite does not produce any rotation. Biot’s law for optical rotation : angle of rotation of the plane of vibration for any given wavelength. : length of the optically active medium traversed. In case of solution or vapours C, C: concentration of the solution or vapour The total rotation produced by a number of optically active substances is equal to the algebric sum of the individual rotations. 1 2 3 .... i i The anticlockwise rotations are taken +ve ; while the clockwise rotations are taken -ve. Applications: 1. To find the percentage of optically active material present in the solution. 2. The amount of sugar present in blood of a diabetic patient determined by measuring the angle of rotation of the plane of polarization. Fresnel’s theory of optical rotation Fresnel’s theory of optical rotation by an optically active substance is based on the fact that any plane polarized light may be considered as resultant of two circularly polarized vibrations rotating in opposite direction with the same velocity or frequency. Fresnel’s theory of optical rotation This explanation was based on the following assumptions: A plane polarized light falling on an optically active medium along its optic axis splits up into two circularly polarized vibrations of equal amplitudes and rotating in opposite anticlockwise. directions–one clockwise and other Fresnel’s theory of optical rotation In an optically inactive substance these two circular components travel with the same speed along the optic axis. Hence at emergence they give rise to a plane polarized light without any rotation of the plane of polarization. Fresnel’s theory of optical rotation In an optically active crystal, like quartz , two circular components travel with different speeds so that relative phase difference is developed between them. If vR>vL the substance is dextro-rotatory And if vR< vL the substance is leavo-rotatory Fresnel’s theory of optical rotation On emergence from an optically active substance the two circular vibrations recombine to give plane polarized light whose plane of vibration has been rotated w.r.t that of incident light through a certain angle depends on the phase diff between the two vibrations. “Fresnel Theory of Rotation” (optic axes perpendicular to refracting face) Plane polarized means resultant of R and L. Note: We can prove it mathematically. Specific rotation The specific rotation of an optically active substance at a given temperature for a given wavelength of light is defined as the rotation (in degrees) produced by the path of one decimeter length in a substance of unit density (concentration) 10 or (If is in cm) C C The unit of specific rotation is deg.(decimeter)-1(gm/cc)-1 T T The molecular rotation is given by the product of the specific rotation and molecular weight of the substance. Polarimeters A device designed for accurate measurement of angle of rotation of plane of vibration of a plane polarized light by an optically active medium is said to be a polarimeter. Two Types: •Laurent's Half shade polarimeter •Bi-quartz polarimeter Laurent's Half shade polarimeter Half shade device-H Glass tube-T1 S V1 N1 H Two nicols- N1 AND N2 T1 N2 T V2 Telescope-T Nicol N2 can be rotated and its position can be noted on a circular scale with verniers V1 and V2 Monochromatic light after passing through N1 become plane polarized with its vibrations in principal plane of nicol. Half shade device (H) • It consists of a circular plate with one half made up of quartz cut parallel to the optic axis which is parallel to YY’ and its thickness is such that it produces a path difference of /2 or a phase difference of between ordinary and extra ordinary components (half wave plate). Y X’ Quartz X Glass Half shade device (H) • Other half is made up of glass, so that glass absorbs same light as quartz plate does. Quartz is a half wave plate. P Principal plane of polarising nicol make an angle with optic axis of quartz plate. Thus direction of vibrations through N1 is along OQ and on passing through glass plate they will remain along OQ. Y Q X’ o Quartz o Glass Y’ On passing through quartz plate it breaks up into e ray component with vibrations parallel to optic axis means parallel to YY’ and o ray component with vibration along XX’. X As they emerges out because of phase change produced between them these combine to form linear resultant vibrations along OP making an angle with YY’. P Y Q X’ X Quartz Glass Y’ When principal plane of nicol N2 is equally inclined to two plane polarized beams means from glass portion and quartz portion Then two parts will appear equally bright or equally dark (Optic axis of N2 is in YY’ or XX’). Laurent's Half shade polarimeter Specific rotation: Half shade device (H) Y 1. Tube is filled with pure water and reading of analyzer is noted for equal illumination 2. Suger sol. is filled in tube, suger sol rotates the plane of vibration of both O coming from quartz and glass equally 3. Note the reading of analyzer for equal illumination again for diff concentration 4. Plot a graph b/w concentration and θ SPECIFIC ROTATION 10 S lC Where l is length of tube T1 in cms. C X Summary: Half shade device (H) Q P Y 1. We use monochromatic source. 2. Half portion is made up of quartz and rest half is of glass. Thickness is in accordance to HWP (means X’ o no use of rotation property). Quartz Glass 3. HWP changes the plane of polarization of incident light (OQ) as OP. Because it creates phase change of π in between e Y’ ray and o ray) . 4. As a result through nicol N2, we can get two semi circles with different intensities (along XX’) and with same intensities (along YY’) too. 5. Sensitively detects the rotation of plane of polarization. X Bi-quartz Device L R t 2 Rotation 1 / This is much more sensitive and accurate then Half shade device polarimeter. But having major drawback for color blindness person. Summary: Bi-quartz Device •White light source is used. •Two semicircular quartz plates (Right and Left handed) with Optic axis perpendicular to crystal surface Y’ (rotation effect only). L •Device is designed for yellow color. •YY’ is tint of passes x R R Y B Y B YR x’ •If Analyzer axes is perpendicular to YY’ then yellow color will be disappeared and we L R t can get resultant of Red and Blue color 2 (Reddish violet color) as min intensity. Rotation 1 / This is much more sensitive and accurate then Half shade device polarimeter. But having major drawback for color blindness person. Daily life uses: Polarization effects in everyday life Communication and radar applications Biology Geology Chemistry Astronomy Materials science Navigation Photography