Light Interference Continued…
description
Transcript of Light Interference Continued…
![Page 1: Light Interference Continued…](https://reader030.fdocuments.us/reader030/viewer/2022033103/56813974550346895da10991/html5/thumbnails/1.jpg)
Light Interference Continued…
![Page 2: Light Interference Continued…](https://reader030.fdocuments.us/reader030/viewer/2022033103/56813974550346895da10991/html5/thumbnails/2.jpg)
Superposition
t
+1
-1
t
+1
-1
t
+2
-2
+
Constructive Interference
In Phase
5
![Page 3: Light Interference Continued…](https://reader030.fdocuments.us/reader030/viewer/2022033103/56813974550346895da10991/html5/thumbnails/3.jpg)
Superposition
t
+1
-1
t
+1
-1
t
+2
-2
+
Destructive Interference
7
Out of Phase
180 degrees
![Page 4: Light Interference Continued…](https://reader030.fdocuments.us/reader030/viewer/2022033103/56813974550346895da10991/html5/thumbnails/4.jpg)
Superposition
+Different f
1) Constructive 2) Destructive 3) Neither
-1.5
-1
-0.5
0
0.5
1
1.5
-1.5
-1
-0.5
0
0.5
1
1.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
10
![Page 5: Light Interference Continued…](https://reader030.fdocuments.us/reader030/viewer/2022033103/56813974550346895da10991/html5/thumbnails/5.jpg)
Interference Requirements
• Need two (or more) waves
• Must have same frequency• Must be coherent (i.e. waves must have definite
phase relation)
12
![Page 6: Light Interference Continued…](https://reader030.fdocuments.us/reader030/viewer/2022033103/56813974550346895da10991/html5/thumbnails/6.jpg)
Interference for Sound …For example, a pair of speakers, driven in phase, producing a tone of a single f and :
l1 l2
But this won’t work for light--can’t get coherent sources
hmmm… I’m just far enough away that l2-l1=/2, and I hear no sound at all!
15
![Page 7: Light Interference Continued…](https://reader030.fdocuments.us/reader030/viewer/2022033103/56813974550346895da10991/html5/thumbnails/7.jpg)
Observe Laser Light Through…
One Slit:
Two Slits:
Multiple Slits:
![Page 8: Light Interference Continued…](https://reader030.fdocuments.us/reader030/viewer/2022033103/56813974550346895da10991/html5/thumbnails/8.jpg)
Observe Laser Light Through…
One Slit: Broad Central Maximum…
Two Slits: Central Bright Spot with
symmetric dark fringes.
Multiple Slits: Central Bright Spot. Narrowor
bright spots, brighter maximums, darker
minimums.
![Page 9: Light Interference Continued…](https://reader030.fdocuments.us/reader030/viewer/2022033103/56813974550346895da10991/html5/thumbnails/9.jpg)
Single Slit Diffraction
![Page 10: Light Interference Continued…](https://reader030.fdocuments.us/reader030/viewer/2022033103/56813974550346895da10991/html5/thumbnails/10.jpg)
Double Slit
Interference Only Interference + Diffraction
![Page 11: Light Interference Continued…](https://reader030.fdocuments.us/reader030/viewer/2022033103/56813974550346895da10991/html5/thumbnails/11.jpg)
Five Slit Diffraction Grating (Inteference & Diffraction)
![Page 12: Light Interference Continued…](https://reader030.fdocuments.us/reader030/viewer/2022033103/56813974550346895da10991/html5/thumbnails/12.jpg)
How do we predict the locations of the bright and dark fringes produced by a single slit? double slit? Multiple slit?
![Page 13: Light Interference Continued…](https://reader030.fdocuments.us/reader030/viewer/2022033103/56813974550346895da10991/html5/thumbnails/13.jpg)
Young’s Double Slit #1
Screen a distance L from slits
Single source of monochromatic light
d
2 slits-separated by d
A. Constructive
B. Destructive
C. Depends on L
The rays start in phase, and travel the same distance, so they will arrive in phase.
L
23
Light waves from a single source travel through 2 slits before meeting on a screen. The interference will be:
![Page 14: Light Interference Continued…](https://reader030.fdocuments.us/reader030/viewer/2022033103/56813974550346895da10991/html5/thumbnails/14.jpg)
Young Double Slit #2
Screen a distance L from slits
Single source of monochromatic light
d
2 slits-separated by d
1) Constructive
2) Destructive
3) Depends on L
The rays start out of phase, and travel the same distance, so they will arrive out of phase.
L
25
½ shift
The experiment is modified so that one of the waves has its phase shifted by ½ . Now, the interference will be:
![Page 15: Light Interference Continued…](https://reader030.fdocuments.us/reader030/viewer/2022033103/56813974550346895da10991/html5/thumbnails/15.jpg)
Young’s Double Slit Concept
Screen a distance L from slits
Single source of monochromatic light
d
2 slits-separated by d
L
At points where the difference in path length is 0, ,2, …, the screen is bright. (constructive)
27
At points where the difference in path
length is
the screen is dark. (destructive)
2
5 ,
23 ,
2
![Page 16: Light Interference Continued…](https://reader030.fdocuments.us/reader030/viewer/2022033103/56813974550346895da10991/html5/thumbnails/16.jpg)
Young’s Double Slit Key IdeaL
30
Two rays travel almost exactly the same distance. (screen must be very far away: L >> d)
Bottom ray travels a little further.
Key for interference is this small extra distance.
![Page 17: Light Interference Continued…](https://reader030.fdocuments.us/reader030/viewer/2022033103/56813974550346895da10991/html5/thumbnails/17.jpg)
d
Path length difference =
d
Young’s Double Slit Quantitative
Destructive interference dsin (m
12)
Constructive interference dsin m
where m = 0, or 1, or 2, ...
d sin
32Need < d
![Page 18: Light Interference Continued…](https://reader030.fdocuments.us/reader030/viewer/2022033103/56813974550346895da10991/html5/thumbnails/18.jpg)
d
Destructive interference dsin (m
12)
Constructive interference dsin m
where m = 0, or 1, or 2, ...
Young’s Double Slit Quantitative
y
sin() tan() = y/L
dLm
y
d
Lmy
21
33
L
A little geometry…
![Page 19: Light Interference Continued…](https://reader030.fdocuments.us/reader030/viewer/2022033103/56813974550346895da10991/html5/thumbnails/19.jpg)
d
L
Young’s Double Slit #3
y
When this Young’s double slit experiment is placed under water. The separation y between minima and maxima
1) increases 2) same 3) decreases
Under water decreases so y decreases35
![Page 20: Light Interference Continued…](https://reader030.fdocuments.us/reader030/viewer/2022033103/56813974550346895da10991/html5/thumbnails/20.jpg)
d
Path length difference d
Double Slit #4
L
= d sin
8
2) dsin (m
12)
1) dsin m
where m = 0, or 1, or 2, ...
Which condition gives destructive interference? d sin()
![Page 21: Light Interference Continued…](https://reader030.fdocuments.us/reader030/viewer/2022033103/56813974550346895da10991/html5/thumbnails/21.jpg)
d
Path length difference 1-2
Multiple Slits: (Diffraction Grating – N slits with spacing d)
L
= d sin
13 dsin mConstructive interference for all paths when
d
Path length difference 1-3= 2d sind
3
Path length difference 1-4= 3d sin
4
1
2
![Page 22: Light Interference Continued…](https://reader030.fdocuments.us/reader030/viewer/2022033103/56813974550346895da10991/html5/thumbnails/22.jpg)
N slits with spacing d
Constructive Interference Maxima are at:
sin m
d
* screen VERY far away
Diffraction Grating
Same as for Young’s Double Slit !
![Page 23: Light Interference Continued…](https://reader030.fdocuments.us/reader030/viewer/2022033103/56813974550346895da10991/html5/thumbnails/23.jpg)
3
23
2 19
3
23
2
dsin
Three slit interference
I0
9I0
![Page 24: Light Interference Continued…](https://reader030.fdocuments.us/reader030/viewer/2022033103/56813974550346895da10991/html5/thumbnails/24.jpg)
For many slits, maxima are still at sin m
d
Region between maxima gets suppressed more and more as no. of slits increases – bright fringes become narrower and brighter.
10 slits (N=10)
dsin
inte
nsi
ty
0
2 slits (N=2)
dsin
inte
nsi
ty
0
Multiple Slit Interference (Diffraction Grating)
22
Peak location depends on wavelength!
![Page 25: Light Interference Continued…](https://reader030.fdocuments.us/reader030/viewer/2022033103/56813974550346895da10991/html5/thumbnails/25.jpg)
Single Slit Interference?!
![Page 26: Light Interference Continued…](https://reader030.fdocuments.us/reader030/viewer/2022033103/56813974550346895da10991/html5/thumbnails/26.jpg)
Wall
Screen with opening (or obstacle without screen)
shadow
bright
This is not what is actually seen!
Diffraction Rays
26
![Page 27: Light Interference Continued…](https://reader030.fdocuments.us/reader030/viewer/2022033103/56813974550346895da10991/html5/thumbnails/27.jpg)
•
•
Diffraction/ HuygensEvery point on a wave front acts as a source of tiny wavelets that move forward.
We will see maxima and minima on the wall.
Light waves originating at different points within opening travel different distances to wall, and can interfere!
30
![Page 28: Light Interference Continued…](https://reader030.fdocuments.us/reader030/viewer/2022033103/56813974550346895da10991/html5/thumbnails/28.jpg)
1st minima
Central maximum
![Page 29: Light Interference Continued…](https://reader030.fdocuments.us/reader030/viewer/2022033103/56813974550346895da10991/html5/thumbnails/29.jpg)
W
w2
sin
W2
1
1
Rays 2 and 2 also start W/2 apart and have the same path length difference.
2
2
1st minimum at sin = /w
When rays 1 and 1 interfere destructively.
w2
sin 2
Under this condition, every ray originating in top half of slit interferes destructively with the corresponding ray originating in bottom half.
Single Slit Diffraction
33
![Page 30: Light Interference Continued…](https://reader030.fdocuments.us/reader030/viewer/2022033103/56813974550346895da10991/html5/thumbnails/30.jpg)
w
Rays 2 and 2 also start w/4 apart and have the same path length difference.
2nd minimum at sin = 2/w
Under this condition, every ray originating in top quarter of slit interferes destructively with the corresponding ray originating in second quarter.
Single Slit Diffraction
4w
1
1
)sin(4w
2
2
When rays 1 and 1 will interfere destructively.
2)sin(
4w
35
![Page 31: Light Interference Continued…](https://reader030.fdocuments.us/reader030/viewer/2022033103/56813974550346895da10991/html5/thumbnails/31.jpg)
Condition for quarters of slit to destructively interfere
sin m
w
(m=1, 2, 3, …)
Single Slit Diffraction SummaryCondition for halves of slit to destructively interfere w
)sin(
w 2)sin(
Condition for sixths of slit to destructively interfere w
3)sin(
38
THIS FORMULA LOCATES MINIMA!!
Narrower slit => broader pattern
All together…
Note: interference only occurs when w >
![Page 32: Light Interference Continued…](https://reader030.fdocuments.us/reader030/viewer/2022033103/56813974550346895da10991/html5/thumbnails/32.jpg)
Recap.• Interference: Coherent waves
– Full wavelength difference = Constructive– ½ wavelength difference = Destructive
• Multiple Slits– Constructive d sin() = m m=1,2,3…)– Destructive d sin() = (m + 1/2) 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() = m m=1,2,3…)– Resolution: Max from 1 at Min from 2
50
op
posi
te!