1. Interference and Diffraction2 2  
Destructive Interference
Constructive Interference

2.  x path difference (x)  phase difference (?) When x < 2 
path difference (x)  phase difference (?)
When x < 
When x  

3. Two oscillators or two sources
To point P d 
dsin
Phase difference when arriving at P is
Original phase difference
phase from path difference

4. What is the result of the sum?
n equally spaced oscillators; equal amplitude; different
in phase (different starting phase, different path length)
E.g. C 2
Plane
wave 1
n slits
equally spaced A B a D E
Huygen’s
wavelets
What is the result of the sum?

5. Using complex amplitude to solve the problem1 1

6. n = 6 Q r T M O

7. n = 6

8. n = 6

9. 1st Constructive Interference:
Path difference C 2 1 A B a …. …. E D
Huygen’s
wavelets
Phase difference
Phase difference …. ….
1st Constructive Interference:
2nd Constructive Interference:
In general, constructive Interference:

10. = I0

11. Width: W10 < W5 ; Height:  n2; Integrated intensity?

12. Fraunhofer Single Slit:
d/2 x x
….. d 

15. } x = 0 and x = d/2; path difference BC = dsin/2.
Interference between
a pair of wavelets
from the top and
center of the slit }
d/2 C B d 
next pair
x = 0 and x = d/2; path difference BC = dsin/2.
 phase difference = (2/)*dsin/2 = dsin/
Destructive interference: dsin/ = , 2, 3, …= n.
 dsin = n.

16. Resolution of single slit and circular aperture:
The Rayleigh Criterion
Well Resolved
Barely Resolved

17. Single Slit:
Circular aperture:
Minimum  1
Airy rings

18. b
The red ones: a
The blue ones: 
n sets of double slits

19. What about n slits each with a slit width of d?

20. If d is very small, upper cap is more flat! a equals to a lot d!

21. Phase difference between different atoms interacted with X-ray.
Diffraction Geometry
1a’, 2a’ 1 X Y 1’ 1a 2’ 2
Plane normal 3 3’   2a X’ Y’ K P M   N d L S 2
Phase difference between different atoms interacted with X-ray.
Atoms in neighboring plane: 2dsin

22. Laue’s Equations: acos0 acos Integer
Constructive interference: |acos-acos0| = h
Similarly in the y direction: |bcos - bcos0| = k
Similarly in the y direction: |ccos - ccos0| = l

23. Reciprocal lattice and diffraction:S S0
OA = pa1+qa2+ra3
p, q, r:integers
S-S0 O   m n -S
Path difference:
uA + Av = Om+On
= S0OA + (-S) OA = (S0-S)OA. v u A If
b1, b2, b3: base vectors of G
 constructive interference

24. Ewald Sphere k k k k |k| = |k| = |k| = 2/ k
Diffraction codition k k
k = G k k k
1/

25. Reciprocal lattice k k k k O