Un-polarized light Ordinary light is a collection of wave trains emitted by atoms or group of atoms with coherent time no longer than 10-8 second. Each wave train has different orientation and phase of the electric field. Consequently, it is a mixture of light polarized in different ways to different degrees, that is, it is randomly polarized or generally referred to as un-polarized light. Plane polarized light If electric field vector of light oscillates in some definite orientation, that is, it oscillates in a fixed plane as light progresses, the light is said to be plane polarized or linearly polarized light. Partially polarized light If a plane or linearly polarized light contains an additional component of natural or randomly polarized light then light is said to be partially linearly polarized light. Elliptically polarized light If electric filed vector rotates on a flattened helix as the wave progresses, that is, electric field vector rotates on the circumference of an ellipse when observed from fixed point in space, the light is said to elliptically By:- Manvendra Singh 1
polarized light. Elliptically polarized light may be left handed or right handed depending on the rotation of the electric field vector in anti-clockwise or clockwise direction when seen towards the source. Left handed elliptical polarization Right handed elliptical polarization Circularly polarized light If the tip of electric field vector of constant magnitude rotates on the helix as the wave progresses, that is, when seen from fixed point in space, the electric field vector appears to rotate on the circumference of a circle, the light is said to be circularly polarized light. If the tip of electric vector when seen towards the wave (source) rotates clockwise, the light is said to be right circularly polarized. On the other hand, if it rotates anticlockwise, the light is said to be left circularly polarized light. Left handed circular polarization By:- Manvendra Singh
Right handed circular polarization The terms plane of vibration and plane of polarization. Plane of vibration The plane containing the direction of vibrations of electric field vectors and the direction of propagation of light in plane polarized light is called as plane of vibration. Plane of polarization The plane perpendicular to the plane of vibration in which components of electric field vectors are zero but contains the direction of propagation of light is called as plane of polarization. Thus, the plane of vibration and the plane of polarization are perpendicular to each other. Brewster s law states that the tangent of the angle of polarization i p for a given reflecting medium is numerically equal to the refractive index of the medium relative to incident medium. That is, tan i p 1 Where, and 1 are refractive indices of reflecting and incident medium respectively. 1 By:- Manvendra Singh 3
Consider incidence of monochromatic light at polarizing angle i p. According to Snell s law of refraction 1sin ip sin r sin ip According to Brewster s law tan ip cosi p 1 Or 1sin ip cos i 3 p Comparing eq and eq 3 cos ip sin r cos r Or ip r 4 That is, reflected and refracted rays are mutually perpendicular at polarizing angle of incidence. Also, as a consequence, we get reflected light as completely plane polarized and refracted light as partially polarized. Law of Malus- According to Malus, when a completely plane polarized light is incident on an analyzer; the intensity I of the emergent light is directly proportional to the square of the cosine of the angle between the planes of transmission of the analyzer and the polarizer. That is, Or I cos I I cos 1 0 Where 0 I is the maximum intensity of the plane polarized light incident on the analyzer. By:- Manvendra Singh 4
To prove this law, let E 0 be the amplitude of the plane polarized light transmitted by the polarizer and incident on the analyzer and be the angle between the plane of transmission of the polarizer and that of the analyzer. The amplitude E 0 may be resolved into two components E cos 0 parallel to the plane of transmission of the analyzer and E sin 0 normal (perpendicular) to it. Because of polarizing ability of the analyzer, only parallel component E cos 0 will be transmitted through the analyzer. Since, intensity is directly proportional to the square of the amplitude, therefore, I E cos 0 Or If k 1, then Or I ke cos 0 I E cos 0 I I cos, where 0 I0 E0 If 0, thencos 1, hence. I I0. Thus, when planes of transmission of polarizer and analyzer are parallel to each other, maximum light is transmitted through the analyzer. If, thencos 0, hence I 0. Thus, when planes of transmission of polarizer and analyzer are perpendicular to each other, no light is transmitted through the analyzer. If un-polarized light is incident on the polarizer, the intensity of light transmitted by the polarizer is one-half the intensity of un-polarized light incident on it. To prove this, let be the angle between the plane of vibration of the electric field vector of the incident light and the plane of transmission of the polarization. According to law of Malus, the intensity of light transmitted by the polarizer will be By:- Manvendra Singh 5
' I0 Iu cos 3 Since, incident light is un-polarized; its electric field vector vibrates randomly in all directions from 0 to. Therefore, the intensity of light transmitted through the polarizer will be the average of eq 3. Hence, I0 I ' 0 = I u cos Solved Important Questions (Physics) B. Tech II Sem 007-08 by Tej Kumar Singhal (IET) 4 Since, cos 1 therefore I I u 0 4 Thus, the intensity of light transmitted through the polarizer and the analyzer is given by I I u cos 5 Where I u is the intensity of incident un-polarized light. Double refraction There are certain transparent substances such as calcite (crystalline CaCO 3 or Iceland spar), topaz, quartz, mica, argonite etc. which forms two images of an object, that is, incident ray splits into two refracted rays. This phenomenon is called as double refraction or birefringence and substances showing this phenomenon are called double refracting crystals. For example, when a calcite crystal is placed on a white paper having a small ink dot, two images of ink dot are seen when viewed through the upper surface of the crystal. If the calcite crystal is rotated about the direction of incident ray; out of two images, one image remains stationary while the other image rotates By:- Manvendra Singh 6
around the stationary image. The first type of image (stationary) is formed by a ray which obeys ordinary laws of refraction (Snell s laws) and is, therefore, called as ordinary ray (o-ray). It always remains in the same plane of incidence and its velocity in crystal is found same in all directions. The second type of image (rotating) is formed by a ray which does not obey ordinary laws of refraction and whose refractive index is a function of direction, that is, its velocity in crystal is found different in different directions, and is, therefore called as extra-ordinary ray (e-ray). When a tourmaline crystal is placed on the calcite crystal and rotated about the direction of incident ray, if intensity of ordinary image decreases, then intensity of extra-ordinary image increases. At one position of the tourmaline crystal, when intensity of ordinary image becomes zero, the intensity of extra-ordinary image becomes maximum. If the crystal is further rotated by 90 degree, then the intensity of ordinary image becomes maximum and that of extra-ordinary image becomes zero. Thus, it is clear that both o-ray and e-ray is plane polarized light and planes of vibration of these rays are perpendicular to each other. Huygens explanation of double refraction Double refraction or birefringence is analyzed in light of Huygens theory which is generalization of the Huygens construction for isotropic media. The basic postulates of this theory of wave front construction are: 1. When a beam of light strikes the surface of double refracting crystal, each point on the surface becomes a source of secondary emission. It originates two types of disturbances: one each corresponding to ordinary ray (o-ray) and extra-ordinary ray (e-ray). By:- Manvendra Singh 7
. For o-ray, the velocity of light is same in all the directions and, therefore, it Spreads on the surface of a sphere, that is, o-wave front is spherical. 3. The crystal is anisotropic for e-ray. Its velocity is same as that of o-ray along The optic axis and differ maximum in the direction perpendicular to optic axis. Thus, e-wave front spreads over the ellipsoid of revolution along optic axis. 4. Since, along the optic axis, ve vo ve vo, e o, the ellipsoid encloses the sphere and touches along optic axis. For positive crystals, the otherwise is true, the sphere encloses the ellipsoid and the two touch along the optic axis. The vibrations of e-ray lie in the principal section but that of o-ray lie perpendicular to it. What are phase retardation plates? and for negative crystal Phase retardation plates When a light ray travels perpendicular to optic axis, the o-wave and e-wave travel in the same direction but with different velocities. Thus, after traveling certain length of the crystal, one wave shall lead in phase to the other wave. Such plates are called phase retardation plates. Consider a monochromatic plane polarized light of wavelength incident normally on a double refracting crystal like calcite, with optic axis parallel to the surface. It splits into o-ray and e-ray which travels in the same direction but with different velocities and the phase of one wave shall retard as compared to the other. In calcite crystal, the velocity v e of e-ray is greater than velocity v o of o-ray. So the difference in time T taken by the two waves to cross the plate of thickness t will be t t T vo ve Therefore, path difference between the e-ray and o-ray will be x t o e Where o and e are refractive indices of calcite for o-ray and e-ray respectively. Hence, the phase difference between the e-ray and o-ray will be x t o e 1 Or Eq 1 represents the relative phase retardation between o-ray and e-ray. By:- Manvendra Singh 8
Two main types of phase retardation plates are: Quarter wave plate and half wave plate. Quarter wave plate (QWP) A plate of double refracting uniaxial crystal of suitable thickness t cut with its optic axis parallel to its refracting faces and capable of producing a path difference of 4 or a phase difference of between two mutually perpendicular o-waves and e-waves is called as quarter wave plate (QWP). For a quarter wave plate 5 9 1,,... n where n 0,1,,3... Comparing above eq with eq 1, we get 4n 1 t o e Or t 4n 1 4 o e 3 Quarter wave plate is used for producing elliptically or circularly polarized light. When a plane polarized light (PPL) is incident normally on a quarter wave plate and its plane of vibration does not makes an angle of 45º with the optic axis, then the emergent light is elliptically polarized light (EPL). When a plane polarized light is incident normally on a quarter wave plate and its plane of vibration makes an angle of 45º with the optic axis, then the emergent light is circularly polarized light (CPL). By:- Manvendra Singh 9
Half wave plate (HWP) - A plate of double refracting uniaxial crystal of suitable thickness t cut with its optic axis parallel to its refracting faces and capable of producing a path difference of or a phase difference of between two mutually perpendicular o-waves and e-waves is called as half wave plate (HWP). For a half wave plate,3,5... n 1 where n 0,1,,3... 4 Comparing above eq 4 with eq 1, we get Or t 1 o e n 1 t n o e Half wave plate is used for changing the direction of plane of vibration of the plane polarized light. When a plane polarized light is incident normally on a half wave plate (HWP), the emergent ray remains plane polarized but the plane of vibration of the emergent ray rotates through an angle from the plane of vibration of incident ray, where is the angle between the plane of vibration of the incident light and the optic axis of a half wave plate. Half wave plate changes left handed elliptically or circularly polarized light into respective right handed elliptically or circularly polarized light and vice-versa. 5 By:- Manvendra Singh 10
Production of elliptically or circularly polarized light Elliptically or circularly polarized light may be produced using an experimental arrangement shown in the figure below. Light from a monochromatic source, say sodium lamp S 1 falls on Nicol prism N 1 which produces plane polarized light. Nicol N is adjusted in crossed position so that the field of view is dark. Now a quarter wave plate (QWP) mounted on a tube T 1, which is free to rotate about the outer tube T, is placed between the crossed Nicol prisms. Due to introduction of quarter wave plate between N 1 and N some light is observed through N. The quarter wave plate is rotated until the field of view is again dark. It means that incident vibrations are making angle 0 or with optic axis. Keeping quarter wave plate fixed, T 1 is rotated so that the mark S on plate coincides with zero mark on T 1. Now by rotating the quarter wave plate, if mark S is made to coincide with 45º or 135º marks on T 1, then the light coming out of quarter wave plate will be circularly polarized. At these positions, the amplitudes of ordinary ray and extra-ordinary become equal. By:- Manvendra Singh 11
For rotation of quarter wave plate by an angle other than 45º will produce elliptically polarized light, that is, amplitudes of ordinary ray and extra-ordinary ray become un-equal. N shall analyze light coming out from quarter wave plate. If on rotating N, intensity varies between maximum and minimum, that is, not equal to zero, then light coming out from quarter wave plate is elliptically polarized light. If it shows no variation in intensity, then light coming out from quarter wave plate is circularly polarized light. Analysis the light of unknown polarization by quarter wave plate (QWP) and rotating Nicol The following can be used to analyze the light of unknown polarization by quarter wave plate and rotating Nicol. By:- Manvendra Singh 1
distinguish quarter wave plate (QWP), plane glass plate and half wave plate (HWP) The following table can be used to distinguish quarter wave plate, plane glass plate and half wave plate. By:- Manvendra Singh 13
Laurent s half-shade polarimeter Laurent s half shade polarimeter is suitable only for one wavelength for which the path difference between o-ray and e-ray is. It is usually constructed for sodium source. When position is adjusted for equally dark halves, it gives fairly accurate observation as slight rotation of the analyzer changes the intensity of two halves. Bi-quartz polarimeter In bi-quartz polarimeter, transition from red to blue is very rapid, hence, zero position can be obtained very accurately. In this polarimeter, white light can be used, that is, mercury lamp can be used. It is highly sensitive device for measuring optical rotation. By:- Manvendra Singh 14
This instrument does not give accurate results for colorless optically active substances due to rotatory dispersion produced by the substance itself. It is not possible for color blind person to use this instrument. By:- Manvendra Singh 15