1. 10B11PH111 WAVE / PHYSICAL OPTICS MODERN PHYSICS INTERFERENCE
DIFFRACTION
POLARIZATION
RELATIVITY
RADIATION
ATOMIC STRUCTURE
STATISTICAL
DISTRIBUTIONS
LASERS
WAVE / PHYSICAL
OPTICS
MODERN
PHYSICS

2. INTERFERENCE
Light + Light = ?????

3. Wave???? There are two types of common waves. Sound wave Light wave
Waves are characterized by crest (highs) and trough(lows)
There are two types of common waves.
Sound wave
Light wave
Wave - A wave is a disturbance that propagates, carrying energy, which can travel through either in a medium or through vacuum, waves can transfer energy from one place to another without any displacement of the particles of the medium.

4. Physical Description of a Wave
frequency
Amplitude
wavelength
phase
Frequency is the measurement of the number of times that event occurs repeatedly per unit time. To calculate the frequency, one fixes a time interval, counts the number of occurrences of the event within that interval, and then divides this count by the length of the time interval. b
Amplitude is a nonnegative scalar measure of a wave's magnitude of oscillation. The y is the amplitude of the wave.
The wavelength is the distance between repeating units of a wave pattern
The phase of a wave relates the position of a feature, typically a peak or a trough of the waveform, to that same feature in another part of the waveform.
waves of various frequencies; the lower waves have higher
frequencies than those above.

5. Phase difference and path difference
The phase difference between two signals of the same frequency can be thought of as a delay or advance in the start of one signal's cycle with respect to another.
Phase difference is expressed in degrees from 0 to 360. If the difference is 180 degrees then the two signals are said to be in antiphase: they are equal but opposite, and if added together will sum to zero. If the phase difference is 90 degrees then the signals are said to be in quadrature.
If the phase difference between two waves is 2 then the path difference between that two waves is .
Let for a path difference x, the phase difference is .
/2
For a path difference , phase difference = 2 
so, for path difference x, the phase difference =
So, phase difference  =

6. Electromagnetic radiation of any wavelength.
What is light?
Electromagnetic radiation of any wavelength.
The three basic dimensions of light :
Intensity
Frequency
Polarization
The three basic dimensions of light :
Intensity (or amplitude, perceived by humans as the brightness of the light),
Frequency (or wavelength, perceived by humans as the color of the light),
Polarization (or angle of vibration and not perceptible by humans under ordinary circumstances)

7. Can two independent sources be coherent????
Coherent Sources
Sources emitting light waves of the same frequency, nearly same amplitude and are always in phase with each other or having a constant phase relationship between them are called Coherent sources
Incoherent sources of light are said to be in coherent if they emit light waves phases changes with time, the phase difference at a point at which they arrive also vary with time in random way. Hence, the intensity at a point will change with time and there will be no modification in intensity due to superposition of waves. In other words, the incoherent waves would not produce any observable interference pattern.
Can two independent sources be coherent????

8. Two ways to get coherent source
Division of wave front.
Young’s double slit
Loyd Mirror
Division of amplitude ( Intensity)
Thin film interference
Two ways to get coherent source
Division of wave front : A narrow source and its virtual image or two virtual images can be used as coherent sources. Two slits illuminated by the light coming through a single slit can be used as coherent sources e.g. Young’s double slit , Fresnel bi-prism etc.
Division of amplitude : the amplitude( Intensity) of a light wave is divided into two parts reflected and transmitted components, by partial reflection at two surfaces. Two reflected beams so produced interfere due to different paths traveled by the two beams leading to an additional path difference. E.g. thin films, Newton’s rings etc

9. Superposition Of Two Waves:
Interference
principle of superposition states that the net displacement at a given place and time caused by two or more waves traversing the same space is the scalar sum of the displacements which would have been produced by the individual waves separately.
Two wave pulses are travelling, one is moving to the right, the other is moving to the left. They pass through each other without being disturbed, and the net displacement is the sum of the two individual displacements.

10. There are two types of interference:
Interference is the superposition of two or more coherent waves resulting in a new wave pattern.
There are two types of interference:
Constructive
Destructive

11. In Phase
This is called
CONSTRUCTIVE
Interference

12. Antiphase
Destructive
Interference

13. n = 0,1,2,… n = 1,2,3,... Condition for constructive interference
n = 0,1,2,…
Condition for destructive interference
/2
n = 1,2,3,...

14. Superposition of two waves: Intensity distribution
Let y1 and y2 are the displacements of two waves coming from S1 and S2 S2

15. 
Resultant Intensity = (Resultant Amplitude) 2
I  cosine square

16. MAXIMA
 Imax > I1+I2
Imax=4a2
MINIMA
Imin =0
 Imin < I1+I2

17. Law of conservation of energy
Iav = 2I
Iav = I1+I2
 Imax > I1+I2
 Imin < I1+I2
This establishes that in the interference pattern, intensity of light is simply being redistributed i.e. energy is being transferred from regions of destructive interference to the regions of constructive interference. No energy is being created or destroyed in the process. Thus the principle of energy conservation is being obeyed in the process of interference of light

18. For incoherent light
= sum of intensity
of constituent waves.

19. Young’s Experiment (Double Slit Expt.)
The rays add up
to produce bright
and dark bands where rays
from S1 and S2 are in or
out of phase when they
get to the screen
Produces
a small region
which mimics
a coherent
light source
Light
Source
The light
from S1 &
S2 are
in-phase

20. Optical path difference between waves

21. Staying Young (R>>d)
r1 and r2 are PARALLEL!!

22. Example 1 Young’s Double-Slit Experiment
Red light (664 nm) is used in Young’s experiment with slits separated
by m. The screen is located a distance 2.75 m from the slits.
Find the distance on the screen between the central bright fringe and
the third-order bright fringe.

23. 2. You are sitting in a closed room with no windows
2. You are sitting in a closed room with no windows. The only light in the room originates from two identical bare, incandescent light bulbs. One is located on the wall to your left; and the other is located on the wall to your right. Bored, you look up at the ceiling and realize there is no interference pattern. Why is there no interference pattern?
a) The two light sources are not polarized.
b) The two light sources are not coherent.
c) The two light sources are in phase.
d) The interference pattern is too small to observe with the naked eye.
e) Interference of light is never observed, but the diffraction of light can easily be observed.

24. 3. In a Young’s double slit experiment, green light is incident of the two slits; and the resulting interference pattern is observed a screen. Which one of the following changes would cause the fringes to be spaced further apart?
a) Move the screen closer to the slits.
b) Move the light source closer to the slits.
c) Increase the distance between the slits.
d) Use orange light instead of green light.
e) Use blue light instead of green light.

25. 4. What happens to the locations of the maxima for double slit interference when the size of the slits is reduced?
a) Reducing the size of the slits has no effect on the locations of the maxima.
b) The distances between the maxima increase as the widths are reduced.
c) The distances between the maxima decrease as the widths are reduced.
d) Reducing the slit size only increases the number of maxima, but the locations of the initial maxima are not changed.
e) Reducing the slit size only decreases the number of maxima, but the locations of the initial maxima are not changed.

26. 6. Without changing the slit width in the double slit experiment, what effect on the interference pattern does reducing the height of the slit have? Assume that the height always remains somewhat larger than the wavelength of light incident on the slits.
a) There is no effect on the pattern.
b) The distances between the maxima will increase.
c) The widths of the maxima will increase.
d) The number of maxima will increase.
e) The height of the maxima will decrease, but there is otherwise no effect.

27. Young’s double slit
x-d/2
x+d/2
d/2
d/2 
Path difference :

28. For a bright fringe, For a dark fringe, Path difference :
For two beams of equal Irradiance (Io)

30. “zeroth order”

31. Position of nth bright fringe on the screen
Position of nth dark fringe on the screen
Distance between any two consecutive bright or dark fringes (Fringe width) 
 
 D
 1/d 

32. Visibility of the fringes (V)
Separation between dark and bright fringes  
Visibility of the fringes (V)
Maximum and adjacent minimum of the fringe system

33. Overview of Young’s (What is ?)

34. White Light in Young’s Experiment
Nature of the fringes????
The figure shows a photograph that illustrates the kind of interference fringes that can result when white light is used in Young’s experiment. Why does Young’s experiment separate white light into its constituent colors? In any group of colored fringes, such as the two singled out, why is red farther out from the central fringe than green is? Why is the central fringe white?
Why does Young’s experiment separate white light into its constituent colors?
why is red farther out from the central fringe than green is?
Why is the central fringe white?

35. The effect of separation between the two sources on the Fringe System
the effect of increasing the slit width on the Fringe System

36. Fresnel biprism O Screen Displacement method Deviation method
Fringes of equal width
It consists of two thin acute angled prisms joined at the bases. It is constructed as a single prism of obtuse angle of 179º. The acute angle  on both side is about 30´.
The prism is placed with the refracting edge in a way such that Sa is normal to the face bc of prism
S is source
S’ and S” are coherent sources (Virtual) obtained through ‘ab’ and ‘ac’ surface of biprism
D= distance of screen from source.
d = distance between the sources S’ and S’’.
Z1 = distance of biprism from source
Z2 = distance of screen from biprism
D= Z1+Z2 Z1 Z2 D 
Screen 
179o
Ques: Can we determine Wavelength of source through this setup ?
Ans: Yes  

37. Displacement Method from magnification formula,
In this method, the distance between the slit and the eye-piece is kept more than four times the focal length of a convex lens of short focal length used so that the two positions of the lens to form the images of S1 and S2 are found. A convex lens of short focal length is placed between the biprism and the eye-piece (as shown in fig. ). By moving the lens along the bed of the bench, two positions L1 and L2 are obtained such that the real images of S1 and S2 are obtained in the eye-piece. Let d1 and d2 be the separations between real images in the positions L1 and L2 of the lens, respectively. If ‘u’ and ‘v’ are the distances of the slit and the eye-piece from the lens in position L1 then from magnification formula, we have
As the two positions of the lens are conjugate, for the second position L2 of the lens, we have
Comparing eqns. (I) and (2), we get
Thus, by measuring d1 and d2, d can be calculated. For accurate measurement of d, the procedure of determining d1 and d2 is repeated at least three times by moving eye-piece into different positions.
from magnification formula,
for L1 we have
Multiplying (1) and (2) we get
Similarly, for L2
Substituting the values of , d and D we can calculate the value of wavelength () of given monochromatic light.

38. Deviation Method For small angles δ is angle of deviation
From right angle triangle and equation (1).
In this method, d can be determined by using the fact that for a prism of very small refracting angle, the deviation  produced is given by z1
Hence
(d1+d2) α1 D z1 α2
If base angles are different, then

39. Fringes with white light
When white light is used the center fringe at O is white since all waves will constructively interfere here while the fringes on the both side of O are colored because the fringe width () depends on wavelength of light.
For green light,
For red light,

40. Summary
Superposition of waves: Interference, Conditions of constructive and destructive interference.
Coherent sources: division of wavefront: Young’s double slit experiment
Intensity distribution on the screen (Superposition of two waves).
Position of nth order bright (or dark) fringe on the screen.
Fresnels’ Biprism: Fringe width, determination of wavelength of light and theoretical approach to calculate distance between the slits ‘d’.
Use of white light source.

41. Numerical
In a certain region of interference 45th order maximum for the wavelength  = 5893 Å are obtained. What will be the order of interference at the same place for (a)  = 4820 Å, (b)  = 7576 Å.
Ans: (a) 55th (b)35th
The inclined faces of a glass prism of refractive index 1.5 make an angle of 1o with the base of the prism. The slit is 10 cm from the biprism and is illuminated by light of  = 5900 Å. Find the fringe width observed at a distance of 1 meter from the biprism.
Ans: Fringe width= mm (Note: Use angle α in radian)

42. In a biprism experiment with sodium light, bands of width 0
In a biprism experiment with sodium light, bands of width mm are observed at 100 cm from the slit. On introducing a convex lens 30 cm away from the slit, two images of the slit are seen 0.7 cm apart, at 100 cm distance from the slit. Calculate the wavelength of sodium light.
Ans: Å
More numerical on
Wave representation; Amplitude, phase, frequency
Intensity distribution; Imax, Imin, …..
Biprism, double slit interference

43. Assignment-1
Show that
Sol:

44. WHAT WILL HAPPEN? In Double slit experiment:
Insert a thin transparent glass sheet of thickness t and refractive index  in the path of one beam.
Fringe pattern will remain same
WHAT WILL HAPPEN? or S1 S2 D d P x
Any change in Fringe pattern t
Because S1P ray will travel more path. hence effective path difference becomes

45. Time required for the light to reach from S1 to the point P is
where ‘c’ is the velocity of light in air and ‘v’ its velocity in the medium
Time required for the light to reach from S2 to the point P is
The path difference (Δ) between the beams reaching P, from S1 and S2

46. So the path difference will be
As we know
So the path difference will be
If P is the centre of the nth bright fringe, then
It means that the introduction of the plate in the path of one of the interfering beams displaces the entire fringe system through a distance
At n = 0 the shift x0 of central bright fringe is
Note: This displacement is towards the beam in the path of which the plate is introduced.

47. D, d,  and t can be calculated
Knowing the shift in central fringe
D, d,  and t can be calculated
We use white light to determine the thickness of the material.
For monochromatic light central fringe will similar to other bright fringe. For white light central fringe is white.
WHY??????

48. Displacement of fringes
Determine condition of net path difference.
µ1,t1 C’ S1 C S2
µ2,t2
Screen
Case 1: If µ1= µ2=µ and t1>t2 , Δ is positive ( upward shift)
or t2>t1 , Δ is negative ( downward shift)
Case 2: If t1=t2= t and 1>2 , Δ is positive ( upward shift)
or 2>1 , Δ is negative ( downward shift)

49. Lloyd’s mirror Nature of the central fringe? Real source Mirror
Light directly coming from the slit S interferes with the light reflected from the mirror forming an Interference pattern in the region OQ of the screen.
Extra phase difference ±p in Lloyd’s mirror. Therefore the central fringe will be dark
Real source
Mirror
Virtual source
Nature of the central fringe?

50. Summary Lecture-1: Introduction Lecture-2:
Superposition of two waves, Imax, Imin.
Double slit experiment (Division of wave front), Expression for fringe width.
Lecture-3:
Fresnel’s Biprism- Determine λ of sodium light.
Displacement of fringes due to one transparent glass sheet.
Displacement of fringes due to two transparent glass sheets.

51. Phase change on Reflection,
Refraction