polarization - birefringence and huygen's theory of double refraction

POLARIZATION ANDHUYGEN’S THEORY OF DOUBLE REFRACTION Anuroop Ashok Ist Yr. B Tech

HISTORICAL CONTEXT•Before the beginning of the nineteenth century, light was considered to be a stream of particles.

• The particles were either emitted by the object being viewed or emanated from the eyes of the viewer.

•Newton was the chief architect of the particle theory of light.• He believed the particles left the object and stimulated the sense of sight upon

entering the eyes

NATURE OF LIGHT• The optical phenomena like interference and diffraction exhibited

by the light establishes its wave nature.• The nature of this wave is given by the phenomena of Polarization.• Light is an ElectroMagnetic Wave and Polarization proves Light to be

a transverse Wave.• Thus Light has an Electric vector (E) and a Magnetic vector(M)

vibrating in perpendicular directions.• Electric field vector is of primary imporatance.

Lights are Electromagnetic Waves

POLARIZATION• Polarization of light waves is the phenomenon of restricting the plane

of vibration of Electric field vector of light in a definite plane.

There are three type of polarized light 1) Plane Polarized Light (ppl or lpl)

2) Circularly Polarized Light (cpl)3) Elliptically Polarized Light (epl)

Polarization – Applications

PRODUCTION OF PLANE POLARIZED LIGHT• 1) By Reflection• 2) By Refraction• 3) By Selective Absorption( Dichroizm )• 4) By Scattering • 5) By Double Reflection

DOUBLE REFRACTION OR BIREFRINGENCE• When ordinary light is allowed to pass through a calcite or quartz , it

splits into two refracted beams(O-ray &E –ray )and both are plane polarized lights.

BIREFRINGENCE

. HUYGEN’S PRINCIPLE • Huygens’ principle, in optics, a statement that all points of a wave front of light in a vacuum or

transparent medium may be regarded as new sources of wavelets that expand in every direction at a rate depending on their velocities.

• “ Every point on a wave-front may be considered a source of secondary spherical wavelets which spread out in the forward direction at the speed of light. The new wave-front is the tangential surface to all of these secondary wavelets.”

• Proposed by the Dutch mathematician, physicist, and astronomer ,Christiaan Huygens, in 1690, it is a powerful method for studying various optical phenomena. A surface tangent to the wavelets constitutes the new wave front and is called the envelope of the wavelets. If a medium is homogeneous and has the same properties throughout (i.e., is isotropic), permitting light to travel with the same speed regardless of its direction of propagation, the three-dimensional envelope of a point source will be spherical; otherwise, as is the case with many crystals, the envelope will be ellipsoidal in shape (see double refraction). An extended light source will consist of an infinite number of point sources and may be thought of as generating a plane wave front.

A wavefront is a surface over which an optical wave has a constant phase. For example, a wavefront could be the surface over which the wave has a maximum (the crest of a water wave, for example) or a minimum (the trough of the same wave) value. The shape of a wavefront is usually determined by the geometry of the source. A point source has wavefronts that are spheres whose centers are at the point source.

HUYGEN’S THEORY OF DOUBLE REFRACTION

•According to Huygen’s theory , a point in a doubly refracting or birefringent crystal produces 2 types of wavefronts:

The wavefront corresponding to the O-ray Spherical wavefrontoThe ordinary wave travels with same velocity in all directions

and so the corresponding wavefront is spherical. The wavefront corresponding to the E-ray Ellipsoidal

wavefrontoExtraordinary waves have different velocities in different

directions, so the corresponding wavefront is elliptical.

WAVE SURFACES FOR NEGATIVE AND POSITIVE CRYSTALS

NEGATIVE CRYSTALS • Negative crystals are crystals in which refractive index corresponding to E-Ray

(nE ) is less than the refractive index corresponding to O-Ray ( nO ) in all directions except for Optic axis.• The E-Ray travels faster than O-Ray except along the Optic axis.• The spherical O-Wavefront is entirely within the ellipsoidal E -Wavefront.• Ex: Calcite , Tourmaline ,Ruby ...

POSITIVE CRYSTALS• Positive crystals are crystals in which refractive for O-Ray is less than that for E-

Ray(nO<nE).• The velocity of O-Ray is greater than or equal to the velocity of E-Ray. • The ellipsoidal E-wavefront is entirely within the spherical O-wavefront.• Example : Quartz (SiO2), Sellaite (MgF2),Rutile (TiO2),…

OPTIC AXIS• Optic axis of a crystal is the direction in which a ray of transmitted light suffers no

birefringence (double refraction). Light propagates along that axis with a speed independent of its polarization.• For all rays not traveling along the optic axis, the velocity is determined by a pair

of refractive indices called the ordinary refractive index no and the extraordinary refractive index ne, and the path of an incident ray is split into two rays, the so-called o-rays and e-rays.• According to number of optic axes crystals are divided as : Uniaxial and Biaxial

crystals.

UNIAXIAL MINERALS•Uniaxial minerals are defined as minerals that have one and only one direction along which light passes with the vibrations (remember, vibrations are always perpendicular to the direction of propagation) moving at equal speed (and hence with a unique resistance or refractive index).

•Uniaxial minerals are ones that crystallize in the tetragonal, hexagonal and trigonal systems.

•Light passing through a uniaxial crystal at an orientation other than the optic axis will therefore break into 2 rays: an ordinary ray “o”, and an extraordinary ray “e”.

•A mineral in which the extraordinary ray is slower than that of the ordinary one (i.e. > ) is considered to be optically positive, and vice versa.

• Examples: Calcite , Quartz

BIAXIAL MINERALS• Are minerals with 2 optic axes; i.e. 2 directions along which the light shows no birefringence

and vibrates in a circular section with a unique constant refractive index. (known as ).• Biaxial minerals are ones that crystallize in the orthorhombic, monoclinic and triclinic systems.• Biaxial minerals have 3 indices of refraction: , , and , listed in order of increasing values (i.e.

is always > > ).The maximum birefringence of a biaxial mineral will be: - . • Light incident along one of the two optic axes will vibrate in one direction only with a refractive

index value given by the radius of the circular section to which it is perpendicular. If has a value closer to than to , the mineral is biaxial positive, and vice versa.

• A light ray incident at any angle to the optic axes will still split into 2 rays. However, unlike in the case of uniaxial minerals, both rays are extraordinary. One of these extraordinary rays will vibrate with a refractive index of a value between and (called ’), the other between and (called ’).

• Examples :

borax, sugar, feldspar, and niter.

BI-AXIAL CRYSTALS

CALCITE CRYSTALS• Calcite is the crystallized form of Calcium Carbonate(CaCO3).• It is the most stable polymorph of Calcium Carbonate( CaCO3).• It is called Iceland Spar due to its large availabilities in Iceland.• Color is white or none, though shades of gray, red, orange, yellow, green, blue,

violet, brown, or even black can occur when the mineral is charged with impurities.• Calcite is transparent to opaque and may occasionally

show phosphorescence or fluorescence.• It exists in nature in several forms but cleaves very perfectly along 3 directions

forming a Rhombohedron.

Calcite or Calcium carbonate (CaCO3)3-fold symmetry CO3 carbonate groups are all in planes normal to the Optic axis.

Large Birefringence

It is possible to cleave calcite and form sharp faces that create a cleavage form (rhombohedron) as shown below possessing faces of a parallelogram with angles of 78.08 and 101.92. There are only two blunt (not sharp) corners (labeled A and B) where the surface planes meet. A line passing through the vertex of each of these blunt corners and oriented so that it makes equal angles with each face (45.5) and each edge (63.8) is clearly an axis of 3-fold symmetry and called the Optical Axis.

A

B

The 3-fold axis is related to the 3-fold symmetry of the CO3 carbonate groups shown previously and the line representing this axis must be then parallel to the optic axis of the crystal, as shown. The direction in which the ray suffer no Double refraction in the crystal is the

Optical Axis .

Any line in the crystal parallel to this direction is also an Optical Axis.

The birefringent property of calcite leads to the formation of two images as shown in examples. The images are related to the existence of ordinary rays (o-rays) and extraordinary rays (e-rays). An analysis of these rays shows that both these rays are linearly polarized.

Colorless Calcite Rhombohedron with a long edge of ~12 cm.

PRINCIPLE SECTION • For the class of crystals called uniaxial, there is only one direction where all light

rays travel along the same path at a constant velocity.• This direction defines the optic axis or principal axis, and any plane that contains

the optic axis is called a principal plane (sometimes called a principal section) - the plane contain optic axis and normal to any cleavage face. The optic axis is not a specific line, but indicates a direction in the crystal where there is no double refraction. • 3 principle sections through a point are observed- one for each pair of opposite

faces.

The o-wave, with its perpendicular polarization, exhibits a single propagation velocity, v. The wave stimulates numerable atoms at the surface producing a source of radiating spherical wavelets, the summation of which leads to a plane wave propagation as in the case of an isotropic medium like glass.

In the above figure, E lies in the principal section, defining the e-wave, and E = E|| + E, where E|| || Optic-axis. Each component will propagate with velocities, v|| and v, respectively. The result is that a point at the interface emits waves that are elongated into an ellipsoid of revolution rather than a spherical shape.

• A Principle section always cut the surfaces of a Calcite crystals in a parallelogram with angles of 109o and 71o.

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