Huygen's theory of double refraction explains the phenomenon of birefringence in crystals like calcite. According to the theory: - Each point in a birefringent crystal produces two types of wavefronts - a spherical wavefront for the ordinary ray and an ellipsoidal wavefront for the extraordinary ray. - The shape of the wavefronts depends on whether the crystal is negative or positive. In negative crystals like calcite, the extraordinary wavefront is outside the ordinary wavefront, while in positive crystals it is inside. - Huygen's principle treats each point on a wavefront as a secondary source of spherical wavelets, and the envelope of these wavelets makes up the

1. POLARIZATION
AND
HUYGEN’S THEORY OF
DOUBLE REFRACTION
Anuroop Ashok
Ist Yr. B Tech

2. 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

4. 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.

5. Lights are Electromagnetic Waves

6. POLARIZATION
• Polarization of light waves is the phenomenon of restricting the plane
of vibration of Electric field vector of light in a definite plane.

7. There are three type of polarized light
1) Plane Polarized Light (ppl or lpl)
2) Circularly Polarized Light (cpl)
3) Elliptically Polarized Light (epl)

9. Polarization – Applications

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

11. 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.

12. BIREFRINGENCE

13. . 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.

14. 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.

15. 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 wavefront
oThe ordinary wave travels with same velocity in all directions and so the
corresponding wavefront is spherical.
 The wavefront corresponding to the E-ray  Ellipsoidal wavefront
oExtraordinary waves have different velocities in different directions, so the
corresponding wavefront is elliptical.

17. WAVE SURFACES FOR NEGATIVE AND
POSITIVE CRYSTALS

19. 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 ...

20. 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),…

21. 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.

22. 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

23. 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.

24. BI-AXIAL CRYSTALS

25. 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.

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

28. 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.

30. 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.

31. 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.

32. 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.

33. 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.

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

35. THANK YOU…