Unit V.pptx Digital Logic And Circuit Design

B. Tech. Applied Physics
BTPH101
Dr. Manvendra Kumar
Shri Vaishnav Vidyapeeth Vishwavidhyalaya, Indore
Shri Vaishnav Institute of Science
Department of Physics

UNIT V Wave Optics 20/06/2022
Introduction to Interference, Fresnel's Bi-prism,
Interference in Thin films, Newton's rings
experiment, Michelson s interferometer and its
‟
application,
Introduction to Diffraction and its Types, Diffraction
at single slit, double slit, resolving power,
Rayleigh criterion, Resolving power of grating,
Concept of polarized light, Double refraction, quarter
and half wave plate, circularly & elliptically polarized
light.

Coherent Sources
Two sources are coherent if the waves they emit
maintain a constant phase relation.
Effectively, this means that the waves do not shift
relative to one another as time passes.
Lasers are coherent sources of light, while incandescent
light bulbs and fluorescent lamps are incoherent
sources.

Lloyd’s Mirror
• An arrangement for
producing an
interference pattern
with a single light
source
• Waves reach point P
either by a direct path
or by reflection
• The reflected ray can
be treated as a ray
from the source S’
behind the mirror

Schematic diagram of an interference experiment with a
Fresnel biprism (FBP).
S, S1, S2 denote the point source and its two virtual images,
respectively. The grey area is the region in which an
interference pattern can be observed.
S1
S2
S3

Combination of Waves
In general, when we combine two waves to form a composite wave,
the composite wave is the algebraic sum of the two original waves,
point by point in space [Superposition Principle].
When we add the two waves we need to take into account their:
Direction
Amplitude
Phase
+ =

The combining of two waves to form a composite wave is called:
Interference
The interference is constructive
if the waves reinforce each other.
+ =
Constructive interference
(Waves almost in phase)

The combining of two waves to form a composite wave is called:
Interference
The interference is destructive
if the waves tend to cancel each other.
+ =
(Close to p out of phase)
(Waves almost cancel.)
Destructive interference

Interference of Waves
+ =
Constructive interference
(In phase)
+ =
( p out of phase)
(Waves cancel)
Destructive interference

When light waves travel different paths,
and are then recombined, they interfere.
Each wave has an electric field whose
amplitude goes like:
E(s,t) = E0 sin(ks-t) î
Here s measures the distance
traveled along each wave’s path.
Mirror
1
2
*
+ =
Constructive interference results when light paths differ
by an integer multiple of the wavelength: s = m 

When light waves travel different paths,
and are then recombined, they interfere.
Each wave has an electric field whose
amplitude goes like:
E(s,t) = E0 sin(ks-t) î
Here s measures the distance
traveled along each wave’s path.
Mirror
1
2
*
Destructive interference results when light paths differ
by an odd multiple of a half wavelength: s = (2m+1) /2
+ =

Coherence: Most light will only have interference for small optical path
differences (a few wavelengths), because the phase is not well defined over a
long distance. That’s because most light comes in many short bursts strung
together.
Incoherent light: (light bulb)
random phase “jumps”

Coherence: Most light will only have interference for small optical path
differences (a few wavelengths), because the phase is not well defined over a
long distance. That’s because most light comes in many short bursts strung
together.
Incoherent light: (light bulb)
Laser light is an exception: Coherent Light: (laser)
random phase “jumps”

l
l/2
l
0
2p
p
p/2
3p/2
Path difference l then phase difference is 2p
Difference between optical path of two rays which are in constant phase
difference with each other reuniting at a particular point is known as path
difference.
p/2
2
x




2
x




We define the phase difference between any two consecutive points in terms of
radians, whereas the path difference is the integral number of wavelengths in a
phase.

Interference in Thin Film: Due to reflected light
After one internal reflection
at CWE get ray CD.
After refraction at D, ray
finally emerges out along DR1
in air.
BR is parallel to DR1.
Effective path difference
between BR and DR1.
Let GH and G1H1 are two surface of transparent film of
uniform thickness t and refractive index m. Ray AB incident
on upper surface. Partly reflected along BR and refracted
along BC.
F

Interfering waves BR and DR1 are
not parallel, but appear to diverge
from a point S.
Interference takes place from S
which is virtual.
Path difference????
22/06/2022

Path difference is
Assignment :
Find the condition for maximum and
minimum intensities .

Diffraction
When light falls on obstacles (whose size is comparable with the
wavelength of light), it bends round the corners of the obstacles
and enters in the geometrical shadow. This bending of light is
called diffraction.
That region which a given type of
radiation would not reach, because of
the presence of an object, if the
effects of diffraction and interference
could be neglected.

A suitable circular grating is called Fresnel zone plate.
A FZP focuses the incoming beam to a point focus.

Difference between Interference and Diffraction

Fraunhofer Diffraction at Single Slit (Normal incidence)

Diffraction
pattern due to
each individual
slit
Interference
pattern due to
diffracted light waves
from the two slits

Intensity distribution due to diffraction
Resultant curve
Intensity distribution due to interference

UNIT V Wave Optics
Introduction to Interference, Fresnel's Bi-prism,
Interference in Thin films, Newton's rings experiment,
Michelson s interferometer and its application,
‟
Introduction to Diffraction and its Types, Diffraction at
single slit, double slit, Resolving power, Rayleigh criterion,
Resolving power of grating,
Concept of polarized light, Double refraction, quarter and
half wave plate, circularly & elliptically polarized light.

Resolving power
The ability of the instrument to produce
their separate pattern is known as resolving
power.
Capacity of an instrument to resolve two points which
are close together.
It is measured by its ability to differentiate two
lines or points in an object.
The greater the resolving power, the smaller the
minimum distance between two lines or points that
can still be distinguished.

These objects are just resolved
43
Two objects are just resolved when the maximum of
one is at the minimum of the other.

Resolving Power
45
To see two objects distinctly, need qobjects > qmin
qmin
qobjects
Improve resolution by increasing qobjects or decreasing qmin
qobjects is angle between
objects and aperture:
qmin is minimum angular separation
that aperture can resolve: D
d
y

The Rayleigh criterion states that two images are
just resolvable when the central maxima of one is
over the first minima of the other in diffraction
pattern
and vice-versa.
Limits of Resolution

A grating is any regularly spaced collection of essentially identical,
parallel, elongated elements. Gratings usually consist of a single set
of elongated elements, but can consist of two sets, in which case
the second set is usually perpendicular to the first.
Resolving power of grating
Equivalent to large
number of slits
A Plane diffraction grating consists of an
optically plane glass plate on which a number of
equidistance and parallel straight lines are
drawn with the help of a diamond tip.
The lines thus divide the glass plate into
opacities and transparencies.
The transparencies, between the ruled
lines act as slits and the ruled lines act as
opaque spaces.

N slit grating
e
The slit width and the opaque space width are denoted as ‘e’ and
‘d’ respectively. The sum (e+d) is called the grating element of a
diffraction grating.

Light is polarized when
its electric fields
oscillate in a single plane,
rather than in any
direction perpendicular
to the direction of
propagation.
Polarization vertical plane and
in a horizontal plane

Polarized light will
not be transmitted
through a polarized
film whose axis is
perpendicular to
the polarization
direction.
Vertically polarized wave passes through
a vertical slit
But a horizontally polarized wave will not

When light passes through a polarizer, only the
component parallel to the polarization axis is
transmitted. If the incoming light is plane-polarized,
the outgoing intensity is:

This means that if initially unpolarized light
passes through crossed polarizers, no light will
get through the second one.

Example: Two Polaroids at 60°.
Unpolarized light passes through two Polaroids; the axis of one is
vertical and that of the other is at 60° to the vertical. Describe
the orientation and intensity of the transmitted light.
I0
I1 I2
The first Polaroid reduces the intensity of the unpolarized light by a factor
of two. The second Polaroid reduces the intensity by another factor of cos2
θ, giving an overall final intensity of 1/8 of the original intensity. The light
will have the polarization of the second Polaroid, 60° to the vertical.

Conceptual Example: Three Polaroids.
When unpolarized light falls on two
crossed Polaroids (axes at 90°), no
light passes through.
What happens if a third Polaroid, with
axis at 45° to each of the other two, is
placed between them?
Solution: The first polarizer
reduces the initial intensity by a
factor of 2. The second reduces it
by a factor of (cos 45°)2
, or
another factor of 2. Finally, the
third polarizer reduces the
intensity by yet another factor of
2, for an overall reduction of a
factor of 8.

Light is also partially polarized
after reflecting from a
nonmetallic surface. At a
special angle, called the
polarizing angle or Brewster’s
angle, the polarization is
100%:
The reflected light is
polarized perpendicular to
plane of incidence.
The angle between the
reflected light and the
refracted light is 90°.
.
=m

Brewster’s Law?
According to Brewster’s law,
When an unpolarized light of known wavelength is incident
on a transparent substance surface, it experiences
maximum plan polarization at the angle of incidence whose
tangent is the refractive index of the substance for the
wavelength.
μ=tan ⁡
i,
Where,
µ = Refractive
index of the
medium.
i = Polarization
angle.


Brewster was able to determine that the refractive
index of the medium is numerically equal to the tangent
angle of polarization.
From Snell’s Law:
μ=sin⁡i / sin⁡r……..1
From Brewster’s Law:
μ=tan ⁡
i=sin⁡i / cos ⁡
i……..2
Comparing both formulas: 1 and 2
cos⁡i=sin ⁡
r =cos⁡(−r)
i=-r or i+r=
As,i+r+=π, so = .
Therefore, the reflected and the refracted rays are at
right angles to each other.


Unit V.pptx Digital Logic And Circuit Design

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