1. The scattering centre becomes a secondary source of radiation

3. Now consider a set of equidistantly spaced correlated secondary sources

17.  ←

19. Zeroth Order

20. 1st Order

21. 1st Order

22. 1st Order

23. 1st Order

24. 2nd Order

25. 2nd Order

26. 2nd Order

27. 2nd Order

28. ←   ←

29. ←  λ
λ = wavelength

30. ←  d λ
λ = wavelength
d = spacing

31. ←  d d λ
λ = wavelength
d = spacing
sin  = λ/d

33.   2λ
sin  = 2 λ/d

34. d 2λ
sin  = nλ/d
dsin  = nλ
d = λ /sin  (for n = 1)

35. General relation sin  = nλ/d3 2 1
General relation sin  = nλ/d

36. General relation sin  = nλ/d

37. General relation sin  = nλ/d

38. General relation sin  = nλ/d

39. General relation sin  = nλ/d

40. General relation sin  = nλ/d

41. General relation sin  = nλ/d

42. General relation sin  = nλ/d

43. General relation sin  = nλ/d

44. General relation sin  = nλ/d

45. General relation sin  = nλ/d

46. Angled faceted surface of the grooves

47. Angled faceted surface of the grooves
Angled faceted surface of the grooves

48. Angled faceted surface of the grooves
Blazed Gratings
By blazing the grating grooves so that the angle between the incident beam and say the 1st order diffracted beam (mean for the various wavelengths) is the mirror reflection angle, most of intensity can be concentrated into the 1st order diffracted beam. 
Angled faceted surface of the grooves

49. Angled faceted surface of the grooves
Blazed Gratings
By blazing the grating grooves so that the angle between the incident beam and say the 1st order diffracted beam (mean for the various wavelengths) is the mirror reflection angle, most of intensity can be concentrated into the 1st order diffracted beam. 
Angled faceted surface of the grooves