Regarding wave optics phy topic

1. Bridge Classes Summer 2021
Wave Optics

2. Lecture-5
Wave Optics
5.1 Coherent Sources and their
production Techniques
5.2 Qualitative idea of Interference:
common examples from daily life
5.3 Qualitative description of Diffraction
with emphasis on grating

3. Wave Optics
•Wave optics is a study concerned with
phenomena that cannot be adequately
explained by geometric (ray) optics.
– Sometimes called physical optics
•These phenomena include:
– Interference
– Diffraction
– Polarization

4. Wave Optics
•The study of these phenomena is essential for the creation of
devices and concepts such as holograms, interferometers,
gratings, thin-film interference, polarizers, coatings for anti-
reflection (AR) and high reflection (HR), quarter-wave plates, and
laser beam divergence in the near and far field.
•Wave optics treats light as a series of propagating electric and
magnetic field oscillations.

5. What Is A Wave?
• There are many examples of waves in daily life:
– Water wave, sound wave, human wave in a
stadium, …, but what is a wave?
• A wave is a propagating disturbance of some
equilibrium state.
• A wave needs a medium, like air, water, people in a
stadium. The medium consists of individual
“particles” which are normally in a “motionless”,
equilibrium state.

6. Sine wave and its properties
• When the particle’s motion is harmonic,
the medium can support the simplest
wave: Sine Wave.
l
Frequency (n) of a Sine Wave = frequency of
every particle’s oscillation frequency.
Wave length (l): the distance from the
nearest particle which does the same oscillation.

7. Wave Optics
•Wave optics is a study concerned with
phenomena that cannot be adequately
explained by geometric (ray) optics.
– Sometimes called physical optics
•These phenomena include:
– Interference
– Diffraction
– Polarization

8. Wave Optics
•The study of these phenomena is essential for the creation of
devices and concepts such as holograms, interferometers,
gratings, thin-film interference, polarizers, coatings for anti-
reflection (AR) and high reflection (HR), quarter-wave plates, and
laser beam divergence in the near and far field.
•Wave optics treats light as a series of propagating electric and
magnetic field oscillations.

9. Wave Optics
•Wave optics is a study concerned with
phenomena that cannot be adequately
explained by geometric (ray) optics.
– Sometimes called physical optics
•These phenomena include:
– Interference
– Diffraction
– Polarization
Introduction

10. Wave Optics
•The study of these phenomena is essential for the creation of
devices and concepts such as holograms, interferometers,
gratings, thin-film interference, polarizers, coatings for anti-
reflection (AR) and high reflection (HR), quarter-wave plates, and
laser beam divergence in the near and far field.
•Wave optics treats light as a series of propagating electric and
magnetic field oscillations.

11. Superposition of Two Waves
• When two waves come together, what
happens?
– The displacement (or disturbances) will add
together (SUPERPOSITION)
– If at a point in the medium, two waves are pulling
in the same direction, the displacement will be
the sum of the two individual displacements.
– If two waves are pulling in the opposite
directions, the resulting displacement is the
difference.

12. Phase Relation
• The result of the superposition of two
waves depends not only on the magnitude
of the waves, but also on the phase
relation.
– When the waves are in phase, the two crests
coincide, they reinforce each other, the net
result is a large net motion.
– When the two waves are out of phase, the
crest of one wave meets the valley of another,
the net result is a cancellation.

13. Example of adding waves

14. Interference
• When two arbitrary waves are superimposed, the
result is very complicated….
• If two waves have the same wavelength, the
locations of reinforcement and cancellation
may be fixed in space for a long time,
making in possible to SEE the superposition.
We call this phenomenon “Interference”
• There are then destructive and constructive
interferences.

15. Interference
•In constructive interference the amplitude of
the resultant wave is greater than that of either
individual wave.
•In destructive interference the amplitude of the
resultant wave is less than that of either
individual wave.
•All interference associated with light waves
arises when the electromagnetic fields that
constitute the individual waves combine.

16. Young’s Double-Slit Experiment:
Schematic
•Thomas Young first
demonstrated interference
in light waves from two
sources in 1801.
•The narrow slits S1 and S2
act as sources of waves.
•The waves emerging from
the slits originate from the
same wave front and
therefore are always in
phase.

17. Resulting Interference Pattern
•The light from the two slits forms a
visible pattern on a screen.
•The pattern consists of a series of bright
and dark parallel bands called fringes.
•Constructive interference occurs where a
bright fringe occurs.
•Destructive interference results in a dark
fringe.

18. Interference Patterns
•Constructive
interference occurs at
point O.
•The two waves travel
the same distance.
– Therefore, they arrive
in phase
•As a result, constructive
interference occurs at
this point and a bright
fringe is observed.

19. Interference Patterns, 2
•The lower wave has to travel
farther than the upper wave to
reach point P.
•The lower wave travels one
wavelength farther.
– Therefore, the waves
arrive in phase
•A second bright fringe occurs
at this position.

20. Interference Patterns, 3
•The upper wave travels one-
half of a wavelength farther
than the lower wave to reach
point R.
•The trough of the upper wave
overlaps the crest of the lower
wave.
•This is destructive
interference.
– A dark fringe occurs.

21. Interference Equations
•For a bright fringe produced by constructive interference, the
path difference must be either zero or some integer multiple
of the wavelength.
•δ = d sin θbright = mλ
– m = 0, ±1, ±2, …
– m is called the order number
• When m = 0, it is the zeroth-order maximum
• When m = ±1, it is called the first-order maximum
•When destructive interference occurs, a dark fringe is
observed.
•This needs a path difference of an odd half wavelength.
•δ = d sin θdark = (m + ½)λ
– m = 0, ±1, ±2, …
Section 37.2

22. Intensity Distribution, Phase
Relationships
•The phase difference between the two waves at P depends on their path
difference.
– δ = r2 – r1 = d sin θ
•A path difference of λ (for constructive interference) corresponds to a phase
difference of 2π rad.
•A path difference of δ is the same fraction of λ as the phase difference φ is of
2π.
•This gives
2 2
sin
π π
φ δ d θ
λ λ
 

23. Light Intensity, Graph
•The interference
pattern consists of
equally spaced fringes
of equal intensity

24. Conditions for Interference
•To observe interference in light waves, the
following two conditions must be met:
– The sources must be coherent.
• They must maintain a constant phase with respect to
each other.
– The sources should be monochromatic.
• Monochromatic means they have a single wavelength.
Section 37.1

25. Coherent light
• If the light is a wave, how come that we don’t see
much of the interference phenomena?
• We need two sources of light with FIXED phase relation.
If the phase is not fixed and it jumps around, the
interference gets washed out. Most of the light sources
have very short memory of phase and are incoherent.
• If two light sources have a fixed phase relation, we call
then Coherent.
• Or in other words two sources are said to be coherent if
they have exactly same frequency, and have zero or
constant phase difference.

26. Coherent Sources
Most of the light sources around us - lamp,
sun, candle etc are combination of multitude
of incoherent sources of light.
Laser is a coherent source i.e. constituent
multiple sources inside the laser are phase-
locked.
We need coherent sources of light in order to
observe effects of certain optical phenomena
like Interference in lab.
Two parallel slits lighted by a laser beam
behind can be said to be two coherent point
sources

27. Producing Coherent Sources
•Light from a monochromatic source is used to
illuminate a barrier.
•The barrier contains two small openings.
– The openings are usually in the shape of slits.
•The light emerging from the two slits is
coherent since a single source produces the
original light beam.
•This is a commonly used method.

28. Diffraction
•If the light traveled in a
straight line after passing
through the slits, no
interference pattern would
be observed.
•From Huygens’s principle
we know the waves spread
out from the slits.
•This divergence of light
from its initial line of travel
is called diffraction.
Section 37.1

29. Diffraction
A wave passing
through a small
opening will diffract,
as shown. This means
that, after the opening,
there are waves
traveling in directions
other than the
direction of the
original wave.

30. Diffraction
Diffraction is why we can hear sound even though
we are not in a straight line from the source –
sound waves will diffract around doors, corners,
and other barriers.
The amount of diffraction depends on the
wavelength, which is why we can hear around
corners but not see around them.

31. Diffraction
To investigate the
diffraction of light, we
consider what happens
when light passes
through a very narrow
slit. As the figure
indicates, what we see
on the screen is a
single-slit diffraction
pattern.

32. Diffraction
This pattern is due to the difference in path
length from different parts of the opening.
The first dark fringe
occurs when:

33. Diffraction
The second dark fringe
occurs when:

34. Diffraction
In general, then, we have for the dark fringes in a
single-slit interference pattern:
The positive and negative values of m account
for the symmetry of the pattern around the
center.
Diffraction fringes can be observed by holding
your finger and thumb very close together (it
helps not to be too farsighted!)

35. The Diffraction Grating
• A (transmission) diffraction grating is an arrangement
of identical, equally spaced parallel lines ruled on
glass.
• A typical diffraction grating will have something
like.600 lines per millimetre
600mm-1
Diffraction
gratings are used
to produce
optical spectra

36. θ
d
C
A
B
Light of wavelength
λ, normal to the grating
Each of the clear spaces
(A,B,C etc) acts like a very
narrow slit and produces its
own diffraction.
The light is from the same
monochromatic source and
therefore is coherent.

37. θ
θ
θ
d
C
A
B
Light of wavelength
λ, normal to the grating
Consider the light which is
diffracted by each slit at
some angle θ to the normal.
The slits are equally spaced
so that if angle θ produces
light that phase at A and B
(and therefore positively
reinforces ) then the light
will also be in phase from
every other slit and also
produce positive
reinforcement.

38. θ
θ
θ
d
C
A
B
Light of wavelength
λ, normal to the grating
N
When the waves reinforce
each other the path
difference AN is a full
number of wavelengths .
That means that
AN =nλ
where n is a whole number
As:
AN = d sin θ
dsinθ = nλ

39. Diffraction Grating
• The angle θ will be slightly different for each
wavelength of light and so the grating
separates white light into its spectrum and
does this much more effectively than a prism.
• The light needs to be focussed with the
eyepiece lens of a telescope or spectrometer (
or the lens of the eye) after it emerges from
the grating.

40. The Diffraction Grating
• A diffraction grating with a large number of
lines produces very sharp maxima and
completely destructive interference at other
angles

41. Physics of diffraction
• Ray Propagation through the grating
α
β0
Β-1
β1
d
Diffracted light
Reflected light
Grating normal
+ -
Incident light
Diffracted light
α
β1
β0
Β-1
Incident light
Grating normal
Diffracted ray
+ -
+
-
A Reflection grating A transmission grating
Light diffracted in the same direction of the incident ray  +ve angle
α > 0, β1 >0
β0 < 0, β-1 < 0

42. Applications
Gratings as Principle used
FILTERS Plane gratings blazed for the wavelength of
unwanted shorter wavelength radiation
ELECTRON MICROSCOPE
CALIBRATION
Replica gratings made from master gratings
so that a space is left between the grooves.
LASER TUNING Plane reflection grating used in littrow mode
BEAM DIVIDERS Symmetrically shaped grooves and laminar
transmission gratings