1. LECTURE ON INTERFERENCE, DIFFRACTION, POLARISATIONBY
KAVITA MONGA (LECTURER-PHYSICS)
GOVT POLYTECHNIC COLLEGE
KHUNIMAJRA,
MOHALI
DATE- 14/2/2013

3. TOPICS TO BE COVERED NATURE OF LIGHT ELECTROMAGNETIC SPECTRUM
INTERFERENCE
DIFFRACTION
POLARISATION
DIFFERENCE BETWEEN INTERFERENCE & DIFFRACTION
APPLICATIONS

4. Light’s Nature Wave nature (electromagnetic wave)
Particle nature (bundles of energy called photons)

5. Past- Separate Theories of Either Wave or Particle Nature
Corpuscular theory of Newton (1670)
Light corpuscles have mass and travel at extremely high speeds in straight lines
Huygens (1680)
Wavelets-each point on a wavefront acts as a source for the next wavefront   

6. Proofs of Wave Nature Thomas Young's Double Slit Experiment (1807)
bright (constructive) and dark (destructive) fringes seen on screen
Thin Film Interference Patterns
Diffraction fringes seen within and around a small obstacle or through a narrow opening

7. Proof of Particle Nature: The Photoelectric Effect
Albert Einstein 1905
Light energy is quantized
Photon is a quantum or packet of energy

8. The Photoelectric Effect
Heinrich Hertz first observed the photoelectric effect in 1887
Einstein explained it in 1905 and won the Nobel prize for this.

9. Light as waves remember c=fλ
So far, light has been treated as if it travels in straight lines.
To describe many optical phenomena, we have to treat light as waves.
Just like waves in water, or sound waves, light waves can interact and form interference patterns.
remember c=fλ 2

10. The Electromagnetic Spectrum
What is the electromagnetic spectrum?

11. The Electromagnetic Spectrum
The energy field created by electricity and magnetism can oscillate and it supports waves that move.
These waves are called electromagnetic waves.

12. The Electromagnetic Spectrum
Electromagnetic waves have both an electric part and a magnetic part and the two parts exchange energy back and forth.
A 3-D view of an electromagnetic wave shows the electric and magnetic portions.
The wavelength and amplitude of the waves are labeled λ and A, respectively.

13. The Electromagnetic Spectrum
The higher the frequency of the light, the higher the energy of the wave.
Since color is related to energy, there is also a direct relation between color, frequency, and wavelength.

14. Speed of Light c = f l Wavelength (m) Speed of light 3 x 108 m/sec
Frequency (Hz)

15. Calculate wavelength
Calculate the wavelength in air of blue-green light that has a frequency of 600 × 1012 Hz.
1) You are asked for the wavelength.
2) You are given the frequency.
3) The speed of light is c = fλ.
4) λ = c ÷ f
= (3 x 108 m/sec) ÷ (600 x 1012 Hz) = 5 x 10-7 m

16. Waves of the electromagnetic spectrum
Visible light is a small part of the energy range of electromagnetic waves.
The whole range is called the electromagnetic spectrum and visible light is in the middle of it.

17. Waves of the electromagnetic spectrum
Radio waves are on the low-frequency end of the spectrum.
Microwaves range in length from apprxi. 30 cm (about 12 inches) to about 1 mm.
The infrared (or IR) region of the electromagnetic spectrum lies between microwaves and visible light.

18. Waves of the electromagnetic spectrum
Ultraviolet radiation has a range of wavelengths from 400 down to about 10 nm.
X-rays are high-frequency waves that have great penetrating power and are used extensively in medical and manufacturing applications.
Gamma rays are generated in nuclear reactions.

20. Interference, Diffraction, and Polarization
What are some ways light behaves like a wave?

21. Interference, Diffraction, and Polarization
In 1807, Thomas Young ( ) did the most convincing experiment demonstrating that light is a wave.
A beam of light fell on a pair of parallel, very thin slits in a piece of metal.
After passing through the slits, the light fell on a screen.
A pattern of alternating bright and dark bands formed is called an interference pattern.

22. INTRODUCTION TO INTERFERENCE
When two or more sets of waves pass through the same medium, they will cross each other. These waves are not aware of the presence of each other. So the effects produced by one wave are independent of the effects due to the other. The behaviour of these two sets of waves is governed by a universal principle known as “ The Principle of Superposition” which states that the net displacement at a point where two different waves are incident in the vector sum of component displacement.
Any wave motion in which the amplitudes of two waves combine will show Interference.

23. INTRODUCTION TO INTERFERENCE
During interference, energy and displacement are redistributed. At some points, displacement and energy become maximum and at other points displacement and energy become minimum.
This modification in the distribution of light energy got by the superposition of two or more waves is called interference.
TYPES OF INTERFERENCE
Constructive Interference
Destructive Interference

24. Water Waves
A wave generator sends periodic water waves into a barrier with a small gap, as shown below.
A new set of waves is observed emerging from the gap to the wall.

25. Interference of Water Waves
An interference pattern is set up by water waves leaving two slits at the same instant.

26. Interference in spherical waves
maximum of wave
minimum of wave
r1=r2 r1 r2
positive constructive interference negative constructive interference destructive interference
if r2-r1=nλ then constructive interference occurs if r2-r1=(n+½)λ the destructive interference occurs

28. light as waves
it works the same as water and sound!

29. Conditions for Interference
If two waves have a definite phase relationship then they are coherent.
Otherwise, they are incoherent (ex: two light bulbs).
For Interference:
The sources must be coherent.
The sources should be monochromatic.

30. Interference Coherence and Monochromatic
No coherence between two light bulbs
coherence - two or more waves that maintain a constant phase relation.
Coherence time
Coherence length
Some later time or distance
monochromatic - a wave that is composed of a single frequency. Heisenberg uncertainty relation.

32. For Constructive Interference:
The waves must arrive to the point of study in phase.
So their path difference must be integral multiples of the wavelength:
DL= nl
n=0,1,2,3,………

33. interference destructive interference constructive interference
at any point in time one can construct the total amplitude
by adding the individual components

34. For destructive interference:
, the waves must arrive to the point of study out of phase.
So the path difference must be an odd multiple of l/2:
DL= n l m=1/2,3/2,5/2,….

35. + + = = λ λ λ λ demo: interference destructive interference
constructive interference
waves ½λ out of phase
waves in phase

36. Two Waves Interfering

37. Thomas Young’s Double Slit Interference Experiment
Showed an interference pattern
Measured the wavelength of the light

38. double slit experiment
•the light from the two
sources
is incoherent
(fixed phase with respect to each other •in this case, there is no phase shift between the two sources
•the two sources of light must have identical wave lengths

39. Young’s Experiment
In Young’s experiment, light from a monochromatic source falls on two slits, setting up an interference pattern analogous to that with water waves.
Light source S1 S2

40. The Superposition Principle
The resultant displacement of two simultaneous waves (blue and green) is the algebraic sum of the two displacements.
The composite wave is shown in yellow.
Constructive Interference
Destructive Interference
The superposition of two coherent light waves results in light and dark fringes on a screen.

41. Young’s Interference Pattern
Constructive
Bright fringe
Destructive
Dark fringe
Constructive
Bright fringe

42. Conditions for Bright Fringes
Bright fringes occur when the difference in path Dp is an integral multiple of one wave length l. l l l p1 p2 p3 p4
Path difference
Dp = 0, l , 2l, 3l, …
Bright fringes:
Dp = nl, n = 0, 1, 2, . . .

43. Conditions for Dark Fringes
Dark fringes occur when the difference in path Dp is an odd multiple of one-half of a wave length l/2. l l p1
n = odd
n = 1,3,5 … p2 p3 p3
Dark fringes:

44. Analytical Methods for Fringesx y
d sin q s1 s2 d q p1 p2
Dp = p1 – p2
Dp = d sin q
Path difference determines light and dark pattern.
Bright fringes: d sin q = nl, n = 0, 1, 2, 3, . . .
Dark fringes: d sin q = nl/2 , n = 1, 3, 5, . . .

45. Analytical Methods (Cont.)x y
d sin q s1 s2 d q p1 p2
From geometry, we recall that:
So that . . .
Bright fringes:
Dark fringes:

46. The third dark fringe occurs when n = 5
Example 1: Two slits are 0.08 mm apart, and the screen is 2 m away. How far is the third dark fringe located from the central maximum if light of wavelength 600 nm is used? x y
d sin q s1 s2 q
n = 1, 3, 5
x = 2 m; d = 0.08 mm
l = 600 nm; y = ?
d sin q = 5(l/2)
The third dark fringe occurs when n = 5
Dark fringes:

47. Example 1 (Cont. ): Two slits are 0
Example 1 (Cont.): Two slits are 0.08 mm apart, and the screen is 2 m away. How far is the third dark fringe located from the central maximum if l = 600 nm?
x = 2 m; d = 0.08 mm
l = 600 nm; y = ? x y
d sin q s1 s2 q
n = 1, 3, 5
y = 3.75 cm

48. Note
The interference is different for light of different wavelengths

49. θ=sin-1(mλ/d) =sin-1(3x600x10-9/0.01) =0.01030 b) Ym = m λL/d
Question
Two narrow slits are illuminated by a laser with a wavelength of 600 nm. the distance between the two slits is 1 cm. a) At what angle from the beam axis does the 3rd order maximum occur? b) If a screen is put 5 meter away from the slits, what is the distance between the 0th order and 3rd order maximum?
a) use dsinθ=mλ with m=3
θ=sin-1(mλ/d) =sin-1(3x600x10-9/0.01) =
b) Ym = m λL/d
m=0: y0=0
m=3: y3=3x600x10-9x5/0.01 =9x10-4 m
=0.9 mm

50. b) travel paths that differ by an odd number of half wavelengths
quiz (extra credit)
Two beams of coherent light travel different paths arriving at point P. If constructive interference occurs at point P, the two beams must:
a) travel paths that differ by a whole number
of wavelengths
b) travel paths that differ by an odd number of half wavelengths

51. Diffraction
Wave bends as it passes an obstacle.

52. Diffraction of Light
Diffraction is the ability of light waves to bend around obstacles placed in their path.
Ocean
Beach
Fuzzy Shadow
Light rays
Water waves easily bend around obstacles, but light waves also bend, as evidenced by the lack of a sharp shadow on the wall.

53. Diffraction Grating What is a diffraction grating?
What are the two types?
A diffraction grating is a slide with a large number of slits. Usually expressed in the number of slits per mm.
transmission and reflection gratings

54. The Diffraction Grating
A diffraction grating consists of thousands of parallel slits etched on glass so that brighter and sharper patterns can be observed than with Young’s experiment. Equation is similar.
d sin q q d
d sin q = nl
n = 1, 2, 3, …

55. Diffraction gratings
A diffraction grating is a precise array of tiny engraved lines, each of which allows light through.
The spectrum produced is a mixture of many different wavelengths of light.

56. How a Diffraction Grating Works
When you look at a diffracted light you see:
the light straight ahead as if the grating were transparent.
a "central bright spot".
the interference of all other light waves from many different grooves produces a scattered pattern called a spectrum.

57. Diffraction Grating

58. Diffraction Grating Large number of equally spaced parallel slits.
Equations are same as for double slit interference but first calculate the d (slit separation) from the grating density, N. d=1/N , N slits per unit length
dsinq=nl
nl = dx L
Constructive (brights) n=0,1,2,3,…..
Destructive (darks) n=1/2, 3/2, 5/2,…..

59. Spectrometer
A spectrometer is a device that measures the wavelength of light.
A diffraction grating can be used to make a spectrometer because the wavelength of the light at the first-order bright spot can be expressed in a mathematical relationship.

60. The Grating Equation 6l 4l 2l 3l 2l The grating equation: l 1st order
d = slit width (spacing)
l = wavelength of light
q = angular deviation
n = order of fringe
2nd order 2l 4l 6l

61. A compact disk acts as a diffraction grating
A compact disk acts as a diffraction grating. The colors and intensity of the reflected light depend on the orientation of the disc relative to the eye.

62. Diffraction through a Narrow Slit
Each part of the slit acts as a point source that interferes with the others.
(Based on Huygens Principle)

63. Pattern of Diffraction of Light through a Narrow Slitx w L

64. Diffraction from Narrow Slit
w sinq=n l
l= n w y L
w: is the width of the slit
Destructive (dark fringes): n=0,1,2,3,….

65. Diffraction for a Circular Opening
Circular diffraction D
The diffraction of light passing through a circular opening produces circular interference fringes that often blur images. For optical instruments, the problem increases with larger diameters D.

66. Example of Diffraction

67. DIFFERENCE BETWEEN INTERFERENCE AND DIFFRACTION
In the interference phenomenon, the superposition is due to two separate wavefronts originating from two coherent sources while in the diffraction phenomenon the superposition is due to secondary wavelets originating from different parts of the same wavefront.
In the interference, the regions of minimum intensity are perfectly dark while in the diffraction, they are not perfectly dark.

68. DIFFERENCE BETWEEN INTERFERENCE AND DIFFRACTION
The width of the fringes in the interference phenomenon is normally equal and uniform while in diffraction, the width between the fringes is never equal.
In the interference phenomenon, all the positions of maxima are of the same intensity, but in the diffraction phenomenon they are of varying intensity.

69. Polarization Polarization is another wave property of light.
The fact that light shows polarization tells us that light is a transverse wave.
Most of the light that you see is unpolarized.
That does not mean the light has no polarization.
Unpolarized light is actually an equal mixture of all polarizations.
We call ordinary light unpolarized because no single polarization dominates the mixture.

70. An easy way to think about polarization is to think about shaking a spring back and forth.
If the spring is shaken up and down it makes vertical polarization.
If the spring is shaken back and forth it makes horizontal polarization.
Waves move along the spring in its long direction.
The oscillation of the wave (and its polarization) is transverse or perpendicular to the direction the wave travels.

71. Polarization Polarization is a vector.
A wave with polarization at 45 degrees can be represented as the sum of two waves.
Each of the component waves has smaller amplitude.
Most of the light that you see is unpolarized.
That does not mean the light has no polarization.
Unpolarized light is actually an equal mixture of all polarizations.
We call ordinary light unpolarized because no single polarization dominates the mixture.

72. Polarization
We saw that light is really an electromagnetic wave with electric and magnetic field vectors oscillating perpendicular to each other. In general, light is unpolarized, which means that the E-field vector (and thus the B-field vector as long as it is perpendicular to the E- field) could point in any direction
E-vectors could point
anywhere: unpolarized
propagation into screen

73. polarized light
¾ light can be linearly polarized, which means that the E- field only oscillated in one direction (and the B-field perpendicular to that)
¾ The intensity of light is proportional to the square of amplitude of the E-field. I~Emax2

74. How to polarize?
¾ absorption
¾ reflection ¾ scattering

75. polarization by absorption
certain material (such as polaroid used for sunglasses) only transmit light along a certain ‘transmission’ axis.
because only a fraction of the light is transmitted after passing through a polarizer the intensity is reduced.
¾ If unpolarized light passes through a polarizer, the intensity is reduced by a factor of 2

76. polarization by reflection
¾ If unpolarized light is reflected, n1
than the reflected light is partially polarized.
¾ if the angle between the reflected ray and the refracted ray is exactly 900 the reflected n2
light is completely polarized
¾ the above condition is met if for the angle of incidence the equation tanθ=n2/n1
¾ the angle θ=tan-1(n2/n1) is called the Brewster angle
¾ the polarization of the reflected light is (mostly) parallel to the surface of reflection

77. Polarization by scattering
¾ certain molecules tend to polarize light when struck by it since the electrons in the molecules act as little antennas that can only oscillate in a certain direction

79. Polarization
A polarizer is a material that selectively absorbs light depending on polarization.
A polarizer re-emits a fraction of incident light polarized at an angle to the transmission axis.
Most of the light that you see is unpolarized.
That does not mean the light has no polarization.
Unpolarized light is actually an equal mixture of all polarizations.
We call ordinary light unpolarized because no single polarization dominates the mixture.

80. Applications of Polarizers
Polarizing sunglasses are used to reduce the glare of reflected light
The LCD (liquid crystal diode) screen on a laptop computer uses polarized light to make pictures.

81. question
vertical
horizontal
direction of polarization of reflected light
Because of reflection from sunlight of the glass window, the curtain behind the glass is hard to see. If I would wear polaroid sunglasses that allow … polarized light through, I would be able to see the curtain much better.
¾ a) horizontally
¾ b) vertically

82. sunglasses
wearing sunglasses will help reducing glare (reflection) from flat surfaces (highway/water)
without
with sunglasses

83. Interference From Single Slit
When monochromatic light strikes a single slit, diffraction from the edges produces an interference pattern as illustrated.
Pattern Exaggerated
Relative intensity
The interference results from the fact that not all paths of light travel the same distance some arrive out of phase.

84. Single Slit Interference Pattern
Each point inside slit acts as a source.
a/2 a 1 2 4 3 5
For rays 1 and 3 and for 2 and 4:
First dark fringe:
For every ray there is another ray that differs by this path and therefore interferes destructively.

85. Single Slit Interference Pattern1 2 4 3 5
First dark fringe:
Other dark fringes occur for integral multiples of this fraction l/a.

86. Example - Monochromatic light shines on a single slit of width 0.45 mm. On a screen 1.5 m away, the first dark fringe is displaced 2 mm from the central maximum. What is the wavelength of the light? q
x = 1.5 m y
a = 0.35 mm
l = ?
l = 600 nm

87. Resolution of Images
Consider light through a pinhole. As two objects get closer the interference fringes overlap, making it difficult to distinguish separate images. d1
Clear image of each object d2
Separate images barely seen

88. Resolution Limit
Images are just resolved when central maximum of one pattern coincides with first dark fringe of the other pattern. d2
Resolution limit
Resolution Limit
Separate images

89. Resolving Power of Instruments
The resolving power of an instrument is a measure of its ability to produce well-defined separate images.
Limiting angle D q
For small angles, sin q  q, and the limiting angle of resolution for a circular opening is:
Limiting angle of resolution:

90. Resolution and Distanceq so p D
Limiting angle qo
Limiting Angle of Resolution:

91. Example - The tail lights (l = 632 nm) of an auto are 1
Example - The tail lights (l = 632 nm) of an auto are 1.2 m apart and the pupil of the eye is around 2 mm in diameter. How far away can the tail lights be resolved as separate images? q so p
Eye D
Tail lights
p = km

92. Summary d sin q q Young’s Experiment:
Monochromatic light falls on two slits, producing interference fringes on a screen. x y
d sin q s1 s2 d q p1 p2
Bright fringes:
Dark fringes:

93. Summary (Cont.) The grating equation: d = slit width (spacing)
l = wavelength of light
q = angular deviation
n = order of fringe

94. Summary (Cont.) Interference from a single slit of width a:
Pattern Exaggerated
Relative Intensity

95. Summary (cont.) q The resolving power of instruments. p D so
Limiting angle qo
Limiting Angle of Resolution:

96. diffraction
In Young’s experiment, two slits were used to produce an interference pattern. However, interference effects can already occur with a single slit.
This is due to diffraction:
the capability of light to be “deflected” by edges/small openings.
In fact, every point in the slit opening acts as the source of a new wave front

98. interference pattern from a single slit
pick two points, 1 and 2, one in
the top top half of the slit, one in the bottom half of the slit. Light from these two points interferes destructively if:
Δx=(a/2)sinθ=λ/2 so sinθ=λ/a
we could also have divided up the slit into 4 pieces:
Δx=(a/4)sinθ=λ/2 so sinθ=2λ/a
6 pieces:
Δx=(a/6)sinθ=λ/2 so sinθ=3λ/a
Minima occur if sinθ=mλ/a m=1,2,3…
In between the minima, are maxima: sinθ=(m+1/2)λ/a m=1,2,3… AND sinθ=0 or θ=0

99. slit width if λ>a sinθ=λ/a > 1 if λ<<a
λ<a : interference
Not possible, so no
sinθ=mλ/a is very small
pattern is seen
patterns
diffraction hardly seen

100. the diffraction pattern
The intensity is not uniform: I=I0sin2(β)/β2 β=πa(sinθ)/ λ
a a a
a a a

101. question
light with a wavelength of 500 nm is used to illuminate a slit of 5μm. At which angle is the 5th minimum in the diffraction pattern seen?
sinθ=mλ/a
θ=sin-1(5x500x10-9/(5x10-6))=300

102. diffraction from a single hair
instead of an slit, we can also use an inverse image, for example a hair!
demo

103. double slit interference revisited
The total response from a double slit system is a combination of two single-source slits, combined with a diffraction pattern from each of the slit due to diffraction
minima asinθ=mλ, m=1,2,3… maxima asinθ=(m+1/2)λ, m=1,2,3… and θ=0
a: width of individual slit
due to 2-slit
interference
maxima dsinθ=mλ, m=0,1,2,3… minima dsinθ=(m+1/2)λ, m=0,1,2,3… d: distance between two slits

104. double-slit experimenta d
if λ>d, each slit acts as a single
if λ<d the interference spectrum
source of light and we get
is folded with the diffraction
a more or less prefect double-slit
pattern.
interference spectrum

105. question
7th
A person has a double slit plate. He measures the distance between the two slits to be d=1 mm. Next he wants to determine the width of each slit by investigating the interference pattern. He finds that the 7th order interference maximum lines up with the first diffraction minimum and thus vanishes. What is the width of the slits?
7th order interference maximum: dsinθ=7λ so sinθ=7λ/d 1st diffraction minimum: asinθ=1λ so sinθ=λ/a
sinθ must be equal for both, so λ/a=7λ/d and a=d/7=1/7 mm

106. diffraction grating consider a grating with
many slits, each separated by d
a distance d. Assume that for each slit λ>d. We saw that for 2 slits maxima appear if:
dsinθ=mλ, m=0,1,2,3…
This condition is not changed for in the case of n slits.
diffraction gratings can be made by scratching lines on glas and are often used to analyze light
instead of giving d, one usually gives the number of slits per unit distance: e.g. 300 lines/mm d=1/(300 lines/mm)= mm

107. separating colors cd’s can act as a diffraction grating
dsinθ=mλ, m=0,1,2,3… for maxima (same as for double slit) so θ=sin-1(mλ/d) depends on λ, the wavelength.
cd’s can act as a diffraction grating

108. question
¾ If the interference conditions are the same when using a double slit or a diffraction grating with thousands of slits, what is the advantage of using the grating to analyze light?
¾ a) the more slits, the larger the separation between maxima.
¾ b) the more slits, the narrower each of the bright spots and thus easier to see
¾ c) the more slits, the more light reaches each maximum and the maxima are brighter
¾ d) there is no advantage

109. question
An diffraction grating has 5000 lines per cm. The angle between the central maximum and the fourth order maximum is What is the wavelength of the light?
dsinθ=mλ, m=0,1,2,3…
d=1/5000=2x10-4 cm=2x10-6 m m=4, sin(47.2)=0.734
so λ= dsinθ/m=2x10-6x0.734/4=3.67x10-7 m=367 nm

110. Reading Question
What was the first experiment to show that light is a wave?
1. Young’s double slit experiment
2. Galileo’s observation of Jupiter’s moons
3. The Michelson-Morley interferometer
4. The Pound-Rebka experiment
5. Millikan’s oil drop experiment

111. Reading Question
What was the first experiment to show that light is a wave?
1. Young’s double slit experiment
2. Galileo’s observation of Jupiter’s moons
3. The Michelson-Morley interferometer
4. The Pound-Rebka experiment
5. Millikan’s oil drop experiment

112. Reading Question What is a diffraction grating?
1. A device used to grate cheese and other materials
2. A musical instrument used to direct sound
3. A plaque with a tiny circular aperture
4. An opaque objects with many closely spaced slits
5. Diffraction gratings are not covered in Chapter 22.

113. Reading Question What is a diffraction grating?
1. A device used to grate cheese and other materials
2. A musical instrument used to direct sound
3. A plaque with a tiny circular aperture
4. An opaque objects with many closely spaced slits

114. Reading Question
When laser light shines on a screen after passing through two closely spaced slits, you see
1. a diffraction pattern.
2. interference fringes.
3. two dim, closely spaced points of light.
4. constructive interference.

115. Reading Question
When laser light shines on a screen after passing through two closely spaced slits, you see
1. a diffraction pattern.
2. interference fringes.
3. two dim, closely spaced points of light.
4. constructive interference.

116. Thanks