3. Assessment Statements AHL Topic 11.3. and SL Option A-4 Diffraction: 11.3.1.Sketch the variation with angle of diffraction of the relative intensity of light diffracted at a single slit. 11.3.2.Derive the formula for the position of the first minimum of the diffraction pattern produced at a single slit. 11.3.3.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 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 B 1 has a greater distance to travel to get to point P than wavelet A 1  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 b = 3λ

32. Diffraction Patterns – Two Slits Supplemental Material d = 4b 4 th 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 11.3. and SL Option A-4 Diffraction: 11.3.1.Sketch the variation with angle of diffraction of the relative intensity of light diffracted at a single slit. 11.3.2.Derive the formula for the position of the first minimum of the diffraction pattern produced at a single slit. 11.3.3.Solve problems involving single-slit diffraction.

38. #1-4 Homework