1. Diffraction, Gratings, Resolving Power
Physics 102: Lecture 21
Diffraction, Gratings, Resolving Power

2. Recall Interference (at least 2 coherent waves)
Constructive (full wavelength difference)
Destructive (half wavelength difference)
Light (1 source, but different paths)
last lecture
Thin Films
Double slit
today
Multiple slit
x-ray diffraction from crystal
Diffraction/single slit 5

3. But first: Thin Film Practice
Example 1 2
n = 1.0 (air)
nglass = 1.5 t
nwater= 1.3
Blue light (lo = 500 nm) incident on a glass (nglass = 1.5) cover slip (t = 167 nm) floating on top of water (nwater = 1.3).
Is the interference constructive or destructive or neither?
d1 = ½
Reflection at air-film interface only
d2 = 0 + 2t / lglass = 2t nglass/ l0= (2)(167)(1.5)/500) =1
Phase shift = d2 – d1 = ½ wavelength 45

4. Young’s double slit/rays
Bright spots
Shadow
This is not what is actually seen!

5. Young’s double slit/Huygens’ principle
Every point on a wave front acts as a source of tiny wavelets that move forward. • • •

6. Young’s double slit/Huygens’ principle
Every point on a wave front acts as a source of tiny wavelets that move forward. •
m = 0
m = +1
m = -1
m = -2
m = +2 θ •

7. Double Slit Review/ACTθ θ d d
Path length difference
= d sinq θ 2) 1)
where m = 0, or 1, or 2, ...
Which condition gives destructive interference?
d sin() 8

8. Multiple Slits: (Diffraction Grating – N slits with spacing d)1 2 4 3 d d
Path length difference 1-2
= d sinq =l d
Path length difference 1-3
= 2d sinq
=2l
Path length difference 1-4
= 3d sinq
=3l
Constructive interference for all paths when 13

9. Same as for Young’s Double Slit !
Diffraction Grating
N slits with spacing d q
* screen VERY far away
Constructive Interference Maxima are at:
Same as for Young’s Double Slit !

10. Preflight 21.1 L 1 2 d 3 d
All 3 rays are interfering constructively at the point shown. If the intensity from ray 1 is I0 , what is the combined intensity of all 3 rays? 1) I ) 3 I ) 9 I0
9% 68% 29%
Each slit contributes amplitude Eo at screen. Etot = 3 Eo. But I a E2. Itot = (3E0)2 = 9 E02 = 9 I0 15

11. ACT/Preflight 21.2 1 2 d 3 d these add to zero
this one is still there! 2 d 3 d
When rays 1 and 2 are interfering destructively, is the intensity from the three rays a minimum? 1) Yes ) No
52% %
Rays 1 and 2 completely cancel, but ray 3 is still there. Expect intensity I = 1/9 Imax 18

12. Three slit interference19

13. Multiple Slit Interference (Diffraction Grating)
Peak location depends on wavelength!
For many slits, maxima are still at
Region between maxima gets suppressed more and more as no. of slits increases – bright fringes become narrower and brighter.
2 slits (N=2)
intensity l 2l
10 slits (N=10)
intensity l 2l
Here do demo using diffraction grating for red and green laser 22

14. X-Ray Diffraction: A technique to study crystal structureθ d θ
Crystal solid such as sodium
Constructive interference:
Mention that this is used by solid state physicists to determine lattice spacing in crystals
in NaCl
1st maximum will be at 100
For =.017nm
X-ray
Measure , determine d 24

15. Single Slit Interference?!

16. Diffraction rays/single slit
Screen with opening (or obstacle without screen)
Bright spot
Shadow
This is not what is actually seen!

17. Diffraction/Huygens’ principle
Every point on a wave front acts as a source of tiny wavelets that move forward. • • • • •
Light waves originating at different points within opening travel different distances to wall, and can interfere!
We will see maxima and minima on the wall.

18. Central maximum
1st minima

19. Single Slit Diffraction1 1 2 2 W
When rays 1 and 1
interfere destructively.
Rays 2 and 2 also start W/2 apart and have the same path length difference.
Under this condition, every ray originating in top half of slit interferes destructively with the corresponding ray originating in bottom half.
1st minimum at sin q = l/w 33

20. Single Slit Diffraction2 2 1 1 w
When rays 1 and 1
will interfere destructively.
Rays 2 and 2 also start w/4 apart and have the same path length difference.
Under this condition, every ray originating in top quarter of slit interferes destructively with the corresponding ray originating in second quarter.
2nd minimum at sin q = 2l/w 35

21. Single Slit Diffraction Summary
Condition for halves of slit to destructively interfere
Condition for quarters of slit to destructively interfere
Condition for sixths of slit to destructively interfere
(m=1, 2, 3, …)
All together…
THIS FORMULA LOCATES MINIMA!!
Preflight 21.3
Narrower slit => broader pattern
Note: interference only occurs when w > l 38

22. ACTS/Preflights 21.4, 21.5
A laser is shined onto a screen through a very small hole. If you make the hole even smaller, the spot on the screen will get:
(1) Larger (2) Smaller
Which drawing correctly depicts the pattern of light on the screen?
(1)
(2)
(3)
(4) 40

23. Diffraction from Circular Aperture
Central maximum
1st diffraction minimum q
Diameter D
light
Maxima and minima will be a series of bright and dark rings on screen
First diffraction minimum is at 41

24. Intensity from Circular Aperture
First diffraction minima 42

25. These objects are just resolved
Two objects are just resolved when the maximum of one is at the minimum of the other. 43

26. Resolving Power To see two objects distinctly, need qobjects > qmin
qobjects is angle between objects and aperture:
qmin
qobjects ≈ tan (d/y)
qmin is minimum angular separation that aperture can resolve:
demo 752; 2 point sources and different size slits D
sin qmin ≈ qmin = 1.22 l/D y d
Improve resolution by increasing qobjects or decreasing qmin 45

27. ACT: Resolving Power
How does the maximum resolving power of your eye change when the brightness of the room is decreased.
1) Increases 2) Constant 3) Decreases
When the light is low, your pupil dilates (D can increase by factor of 10!) But actual limitation is due to density of rods and cones, so you don’t notice an effect! 47

28. Recap. Interference: Coherent waves Multiple Slits
Full wavelength difference = Constructive
½ wavelength difference = Destructive
Multiple Slits
Constructive d sin(q) = m l (m=1,2,3…)
Destructive d sin(q) = (m + 1/2) l 2 slit only
More slits = brighter max, darker mins
Huygens’ Principle: Each point on wave front acts as coherent source and can interfere.
Single Slit:
Destructive: w sin(q) = m l (m=1,2,3…)
Resolution: Max from 1 at Min from 2
opposite! 50

29. See you Monday!