PHYS 260 Lecture Notes - Lecture 6: Total Internal Reflection, Fiberscope, Optics Algorithm
25 May 2018
School
Department
Course
Professor
FIBER OPTICS
O1.
INTRODUCTION
The transmission of light along transparent cylinders by multiple total internal
reflections is a fairly old and well-known phenomenon. John Tyndall at the Royal
Society in England gave the earliest recorded scientific demonstration of this
phenomenon in 1870. The interest in this phenomenon described by Tyndall was
dormant until 1927. When the possibility of using fibers for transmitting television
pictures was tried out. However these ideas were not pursued. A new burst of
activity began in the early 1950’s when the transmission of pictures along an aligned
bundle of flexible glass fibers was carried out with remarkable success. This led to
the development of ‘flexible fiberscope’. Thus the subject of fiber optics was
established with the advent of lasers, the subject of fiber optics received an added
impetus. Currently throughout the world fiber optics are flexible hair thin threads of
glass or plastic.
O2.BASIC PRINCIPLE: TOTAL INTERNAL REFLECTION
For the phenomenon of TIR to take place the two conditions are to be satisfied
1. Light should travel from denser medium to rarer medium.
2. The angle of incidence should be greater than the critical angle θ
c
of the medium.
Critical angle θ
c
of a medium is the value of the incident angle at which the angle
of refraction is 90
o
.
Consider n
1
is the refractive index of denser medium and n
2
is the refractive index of
rarer medium.
When a light ray traveling in a medium of refractive index n
1
strikes a second medium
of refractive index n
2
the angle of refraction θ is given by Snell’s law n
1
Sin i = n
2
Sin
θ when a ray of light traveling from a optically dense medium to a less dense medium;
n
2
n
1
n
2
n
2
n
1
n
1
When i < θ
c
it is refracted
When i = θ
c
it is traverses along the interface
When i > θ
c
it is total internal reflected
It will not be refracted if it strikes the surface at an angle equal to or greater than a
particular angle called critical angle. Instead it will be totally reflected at the surface
between the two media such a phenomenon occurs because when a ray of light travels
from D.M. to L:DM the refracted ray bends away from the normal. Consider the case
θ = 90
o
n
1
Sin θ
c
= n
2
Sin 90
o
Sin θ
c
= n2/n1 . Thus for any ray whose
angle of incidence is greater than this θ
c
. Total internal Reflection occurs.
O3.Fibre Construction
It consists of a central cylinder or core surrounded by a layer of material called the
cladding, which in turn is covered by a jacket. Light is transmitted within the core the
cladding keeps the light waves within the core. The cladding is having less refractive
index protects than core. The cladding also provides some strength to the core. The
additional jacket protects the fiber from moisture and abrasion.
The core as well as the cladding is made of either glass or plastic with these materials
three major types of fibers are made.
1. Plastic core with plastic cladding
2. Glass core with plastic cladding
3. Glass core with glass cladding.
The cladding is generally silicone or Teflon. The glass is made of silica small
amounts of components such as boron, germanium or phosphorous is added to change
refractive index of the fiber core diameters range from 5 to 600 µm. Cladding
diameters range from 125 to 750µm. Optical fiber diameter is of the order of 0.1 mm.
O4 Numerical Aperture And Acceptance Angle
In optical fibers n
1
> n
2
. In a step index fiber the refractive index is constant
throughout the core. In such a fiber the refractive index profile abruptly changes at
the junction of the core and the cladding because of the abrupt change they are called
step index optical fiber. In a graded index optical fiber refractive index varies
continuously across the core. It is highest of the centre of the core and tapers off
rapidly towards the outer edge.
Core Cladding Silicon Coating Buffer members Strength members Outer Jacket
Let us consider the special case of a ray which suffers critical incidence of the core
cladding interface. The ray to begin with travels along AO entering into the core at an
angle θ
o
to the fiber axis. Let it be refracted along OB at an angle θ
1
in the core and
further proceed to fall at critical angle of incidence (equal to 90-θ
1
) at B on the
interface between core and cladding. Since it is critical angle of incidence, the ray is
refracted at 90
o
to the normal drawn to the interface i.e. it grazes along BC.
Now it is clear from the figure that any ray that enters into the core at an angle of
incidence less that θ
o
will have refractive angle less than θ
o
will have refractive angle
less than θ
1
because of which angle of incidence (=90 – θ
1
) at the interface will
become greater than the critical angle of incidence and thus undergoes total internal
reflection.
On the other hand any ray which enters at an angle of incidence greater than θ
o
at O,
will ultimately be incident at B at an angle less than the critical angle because of
which it will be refracted into the cladding region and thus will be lost.
Now if OA is rotated around the fibre axis keeping θ
0
same, then it describes a
conical surface. We can therefore say that if a beam converges at a wide angle into
the core then only those rays which are funneled into the fiber within this cone will
only be totally internally reflected and thus confined within the fiber for propagation
and the rest of the incident light rays emerge from the sides of the fiber.
The angle θ
0
is called the wave guide acceptance angle, or the acceptance cone half
angle, and Sin θ
0
is called the numerical aperture (N.A.) of the fiber. The numerical
aperture represents the light-gathering capability of the optical fiber.
Condition for propagation:
Let n
0
, n
1
and n
2
be the refractive indices of surrounding medium, core of the fiber,
and cladding respectively.
Now for refraction at the point of entry of the ray A
0
into the core, we have by
applying the Snell’s law that n
o
Sinθ
0
= n
1
Sinθ
1
------- (1). At the point B on the
surface, the angle of incidence = 90-θ
1
. again applying Snell’s law, we have
n
1
Sin(90-θ
1
) =
n
2
Sinθ90 or n
1
Cos
θ
1
=
n
2
or Cos θ
1
=n
2
/n
1
--------- (2).
Cladding
Cladding
Core
Document Summary
The transmission of light along transparent cylinders by multiple total internal reflections is a fairly old and well-known phenomenon. Society in england gave the earliest recorded scientific demonstration of this phenomenon in 1870. The interest in this phenomenon described by tyndall was dormant until 1927. When the possibility of using fibers for transmitting television pictures was tried out. A new burst of activity began in the early 1950"s when the transmission of pictures along an aligned bundle of flexible glass fibers was carried out with remarkable success. This led to the development of flexible fiberscope". Thus the subject of fiber optics was established with the advent of lasers, the subject of fiber optics received an added impetus. Currently throughout the world fiber optics are flexible hair thin threads of glass or plastic. Critical angle c of a medium is the value of the incident angle at which the angle of refraction is 90o. n2 n1.
