light interference continued…. superposition t +1 t +1 t +2 -2 + constructive interference in...
TRANSCRIPT
Light Interference Continued…
Superposition
t
+1
-1
t
+1
-1
t
+2
-2
+
Constructive Interference
In Phase
5
Superposition
t
+1
-1
t
+1
-1
t
+2
-2
+
Destructive Interference
7
Out of Phase
180 degrees
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
Interference Requirements
• Need two (or more) waves
• Must have same frequency• Must be coherent (i.e. waves must have definite
phase relation)
12
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
Observe Laser Light Through…
One Slit:
Two Slits:
Multiple Slits:
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.
Single Slit Diffraction
Double Slit
Interference Only Interference + Diffraction
Five Slit Diffraction Grating (Inteference & Diffraction)
How do we predict the locations of the bright and dark fringes produced by a single slit? double slit? Multiple slit?
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:
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:
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
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.
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
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…
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
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()
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
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 !
3
23
2 19
3
23
2
dsin
Three slit interference
I0
9I0
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!
Single Slit Interference?!
Wall
Screen with opening (or obstacle without screen)
shadow
bright
This is not what is actually seen!
Diffraction Rays
26
•
•
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
1st minima
Central maximum
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
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
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 >
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!