1. Wave Interference and Diffraction

2. 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.

3. A new set of waves is observed emerging from the gap to the wall.
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.

4. Figure 2 on p. 459- both waves encounter same obstacle (blue object)
Figure 2A
Figure 2B
Short wavelengths
Less diffraction (red arrows)
Longer wavelengths
Greater amount of diffraction (red arrows)
Figure 3 on p all 3 diagrams have the same slit opening. The wavelength increases from a-c, so does the amount of diffraction
Figure 4 on p Fig 4a and b have a wave with the same wavelength, however slit opening decreases. As slit width decreases, diffraction increases, as wavelength is kept constant.

5. Interference of Water Waves
Interference occurs when 2 waves in the same medium interact.

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

7. Constructive Interference- two interfering waves have displacement in the same direction. The waves must be in phase and combine together.
Destructive Interference- two interfering waves have displacement in opposite directions when they superimpose. The amplitude of the superimposed wave is smaller then the interacting waves.

8. Constructive Interference Destructive Interference

9. 3 conditions for Interference to occur:
Short distance apart, so they can interact in same medium.
Waves come together at a common point.
Waves must have same frequencies and fixed positions.

10. 2 Point Source Interference
Continuous interference from two sources.
If the source of waves produces circular waves, then the waves will meet within the medium to produce a pattern.
The pattern is characterized by a collection of nodes and antinodes referred to as antinodal lines and nodal lines.
Figure 8 on p. 463

11. Two Point Interference Pattern
When we have two identical point sources that are side by side, in phase, and have identical frequencies, we can analyse the interference pattern that is produced to learn more about the waves.
ripple tank simulation of two point source pattern:

12. Two Point Interference Pattern
Antinodes
Nodes
Sources

13. Two Point Interference Pattern
Thin line = trough
In the diagram, crests are represented by thick lines and troughs are represented by thin lines. We get constructive interference then whenever a thick line meets thick line, or when a thin line meets a thin line. This constructive interference causes antinodes, shown by the red dots.
Thick line = crest

14. Two Point Interference Pattern
Destructive interference occurs whenever a thick line meets a thin line. These points form nodes, which are represented by a blue dot. The nodes and antinodes appear to ‘stand still’ which makes this a standing wave pattern.

15. Two Point Interference Pattern
The number of nodal lines increases when you do any of the following:
Increase frequency of the sources
Decrease the wavelength of the waves
Increase separation between the sources

16. -

17. Young’s Experiment
In 1801 Thomas Young was able to offer some very strong evidence to support the wave model of light.
He placed a screen that had two slits cut into it in front of a monochromatic light.
The results of Young's Double Slit Experiment should be very different if light is a wave or a particle.

18. Light as a Particle

19. Light as a Wave

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

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

22. Interference of the waves determines the intensity of the light.
The alternating areas of dark and light fringes are created by alternating areas of constructive and destructive interference.

23. Conditions for Bright Fringes
Bright fringes occur when the difference in path is an integral multiple of one wave length l. l l l p1 p2 p3 p4

24. What does this mean? Waves must be in phase
Path length needs to be a whole number wavelength difference for constructive interference to occur.
FORMULA for bright fringes, also known as MAXIMA (ON BOARD)

25. Conditions for Dark Fringes
Dark fringes occur when the difference in path 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

26. What does this mean? Waves must be out of phase
Path length needs to be a half number wavelength difference for destructive interference to occur.
FORMULA for dark fringes, also known as MINIMA (ON BOARD)

28. 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, …

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

30. To find slit separation, we take reciprocal of 300 lines/mm:
Example 2: Light (600 nm) strikes a grating ruled with 300 lines/mm. What is the angular deviation of the 2nd order bright fringe?
To find slit separation, we take reciprocal of 300 lines/mm:
300 lines/mm
n = 2
Lines/mm  mm/line

31. Angular deviation of second order fringe is:
Example (Cont.) 2: A grating is ruled with 300 lines/mm. What is the angular deviation of the 2nd order bright fringe?
300 lines/mm
n = 2
l = 600 nm
Angular deviation of second order fringe is:
q2 = 21.10

32. 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.

33. 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.

34. When looking at single slit diffraction we must assume:
Slit width is narrow enough for diffraction to occur. (NOT too small as thought it acts like a point source)
Light is monochromatic with a λ.
Light source is far enough from the slit to ensure all rays hitting the slit are parallel.

36. The pattern observed from single slit diffraction is called Fraunhofer diffraction. (fig.2 p. 512)
This pattern shows a bright central fringe called the central maximum and is flanked by less bright fringes called secondary maxima and dark fringes called minima.
Huygen’s Principle helps to explain and predict the diffraction patterns. All points on a wave front can be thought of as new sources of spherical waves called wavelets. (diagram on board)

37. 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.

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

39. Example 3: Monochromatic light shines on a single slit of width 0
Example 3: 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

40. 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.

41. 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

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

43. 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:

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

45. Example 4: The tail lights (l = 632 nm) of an auto are 1
Example 4: 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

46. Summary 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:

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

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

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

50. CONCLUSION: Chapter 37 Interference and Diffraction