1. Devil physics The baddest class on campus IB Physics

2. Tsokos Lesson 4-7 Diffraction

3. Assessment Statements
AHL Topic and SL Option A-4 Diffraction:
Sketch the variation with angle of diffraction of the relative intensity of light diffracted at a single slit.
Derive the formula for the position of the first minimum of the diffraction pattern produced at a single slit.
Solve problems involving single-slit diffraction.

4. Objectives
Understand diffraction and draw the different diffraction patterns from a rectangular slit, a sharp edge, a thin tube, and a circular aperture
Appreciate that the first minimum in single- slit diffraction past a slit of width b is approximately at an angle θ = λ/b

5. Objectives
Draw the intensity patterns for a single slit of finite width and for two slits of negligible width
Show the effect of slit width on the intensity pattern of two slits

6. Reading Activity Questions?

7. Introductory Video: Diffraction of Light

8. Diffraction
The spreading of a wave as it goes past an obstacle or through an aperture
Value of the wavelength in comparison to the obstacle or aperture defines the diffraction pattern

9. Case 1: Wavelength Much Smaller Than Aperture
Virtually no diffraction takes place

10. Case 2: Wavelength Comparable to or Bigger than Aperture
Diffraction takes place
‘Comparable’ means a few times smaller to slightly larger than

11. Diffraction Around an Obstacle
Sound, with a much larger wavelength, will diffract around the corner of a building but light will not

12. Case 1: Wavelength Much Smaller Than Obstacle
Virtually no diffraction takes place

13. Case 2: Wavelength Comparable to or Bigger than Obstacle
Diffraction takes place
‘Comparable’ means a few times smaller to slightly larger than

14. Diffraction Patterns
When light is diffracted, both constructive and destructive interference occurs

15. Diffraction Patterns
Diffraction is appreciable if wavelength, λ, is of the same order of magnitude as the opening, b, or bigger

16. Diffraction Patterns
Diffraction is negligible if wavelength, λ, is much smaller than the opening, b

17. Huygen’s Principle and Diffraction
Every point on a wavefront acts as a secondary source of coherent radiation
Each point forms its own wavelet
These wavelets will interfere with each other at some distant point

18. Huygen’s Principle and Diffraction
Because of the diffraction angle, wavelet B1 has a greater distance to travel to get to point P than wavelet A1
This results in the wavelets arriving at point P out of phase with each other

19. Huygen’s Principle and Diffraction
If the difference is equal to half a wavelength, the wavelets are 180° out of phase and they completely cancel each other through superposition

20. Huygen’s Principle and Diffraction
If the difference is equal to one entire wavelength, the wavelets are in phase and they form a wavelet of double the original amplitude

21. Huygen’s Principle and Diffraction
Everything in between will show varying levels of constructive and destructive interference

22. Huygen’s Principle and Diffraction
Since the two triangles in the diagram are similar triangles, the same interference pattern will result at point P from all pairs of wavelets

23. Huygen’s Principle and Diffraction
If we approximate AP and BP to be parallel since P is distant and ACB to be a right angle, then

24. Huygen’s Principle and Diffraction
Destructive interference occurs when BC is equal to one half wavelength, then

25. Huygen’s Principle and Diffraction
If we divide the slit into 4 segments instead of two, then

26. Huygen’s Principle and Diffraction
In general, destructive interference occurs when,
This equation gives the angle at which minima will be observed on a screen (P) behind an aperture of width b through which light of wavelength λ passes

27. Huygen’s Principle and Diffraction
Since the angle θ is typically small, we can approximate sin θ ≈ θ (if the angle is in radians), so the first minima would fall at
And for circular slits the formula becomes

28. Diffraction Patterns Minima (blank spaces) appear in pairs
Maxima (bright spaces) appear about halfway between minima
Smaller slit means larger central maximum
b = 2λ
b = 3λ

29. Diffraction Patterns
If λ > b, then sin  > 1 which is impossible, i.e.,  does not exist
The central maximum is so wide that the first minima does not exist
If λ ≈ b, then several minima and maxima exist
If λ « b, then sin   o which means   0 which means the light passes straight through without bending

30. Single-Slit Diffraction Video

31. Diffraction Patterns – Two Slits Supplemental Material
With two slits, interference based on
Interference pattern from one slit alone
Interference coming from waves from different slit
d = 16λ
d = 16λ
b = 3λ

32. Diffraction Patterns – Two Slits Supplemental Material
d = 4b
4th maximum missing

33. Summary Video

34. Σary Review
Do you understand diffraction and draw the different diffraction patterns from a rectangular slit, a sharp edge, a thin tube, and a circular aperture?
Do you appreciate that the first minimum in single-slit diffraction past a slit of width b is approximately at an angle θ = λ/b?

35. Σary Review
Can you draw the intensity patterns for a single slit of finite width and for two slits of negligible width?
Can you show the effect of slit width on the intensity pattern of two slits?

36. Assessment Statements
AHL Topic and SL Option A-4 Diffraction:
Sketch the variation with angle of diffraction of the relative intensity of light diffracted at a single slit.
Derive the formula for the position of the first minimum of the diffraction pattern produced at a single slit.
Solve problems involving single-slit diffraction.

37. Questions?

38. Homework
#1-4