wave nature of light thin films, diffraction
DESCRIPTION
Wave nature of light thin films, diffraction. Physics 123, Spring 2006. Intensity in Young’s experiment. E=E 1 +E 2 E=E 0 (sin( w t)+sin( w t+ d )). q =0 d =0: amplitude E( q =0)=2E 0 I( q =0)=4E 0 2 Amplitude E( q )=2E 0 cos( d /2) I( q )=4E 0 2 cos 2 ( d /2). - PowerPoint PPT PresentationTRANSCRIPT
04/19/23 Lecture VI 1
Physics 123, Spring 2006
Wave nature of lightthin films, diffraction
04/19/23 Lecture VI 2
Intensity in Young’s experiment• E=E1 +E2
• E=E0 (sin(t)+sin(t+))
2
cos2
sin2sinsinBABA
BA
2cos
2sin2 0
tEE
2EI =0 =0: amplitude
E(=0)=2E0
• I(=0)=4E02
• Amplitude E()=2E0cos(/2)
• I()=4E02 cos2(/2)
04/19/23 Lecture VI 3
Intensity in Young’s experiment• I(=0)=4E0
2
• I()=4E02 cos2(/2)
y
L
d
I
I
22 cos
2cos
)0(
)(
yL
d
2
md
Ly
mmyL
d
3,2,1,0,• Bright when cos=1, or -1
04/19/23 Lecture VI 4
Young’s experiment r=700 nm b=400 nm• d=2000nm• L=20cm • First fringes (bright
spots) yr, yb-?• m=1:• y=L /d• yr=7cm• yb=4cm• Blue is closer to the
center than red
04/19/23 Lecture VI 5
Young’s experiment
• Two different -
• Distance between slits – d• Multiple slits (diffractive
grating)– same pattern, sharper lines
• Interference pattern depends on – Maxima:– d sin = m
– d sin = m
04/19/23 Lecture VI 6
Coherence
• Why do not we observe an interference pattern between two different light bulbs?
• These two sources of light are incoherent:
• What does it mean for two sources to be coherent?– Same (or close) frequency – Constant shift in phase (not necessarily zero)
04/19/23 Lecture VI 7
Light in a medium (refraction)• Huygens principle
– each point forces oscillations with frequency f
• f1=f2
• v1=c/n1
• v2=c/n2
• n11=n22
• E.g. go from air to medium n:
/n• n=/n
n1
n2
04/19/23 Lecture VI 8
Light in medium
n=2
=400nmx=600nm
n=n400/2=200nm
Destructiveinterference
+
+
-
-
1=k1x=(2/)x=2600/400=3
Extra phase =3
2=k2x=(2/)x=2600/200=60
0)2/3cos()2/cos(
21
EE
04/19/23 Lecture VI 9
Reflection of a transverse wave pulse
•Reflection from fixed end –inverted pulse
•Reflection from loose end – the pulse is not inverted.
04/19/23 Lecture VI 10
Reflection
• Reflect from medium with higher n2>n1 phase change by =
– + -
• Reflect from medium with lower n2<n1 no phase change =0
– + +
+
- +
+
04/19/23 Lecture VI 11
Soap film• Soap film, air on both sides
• Thickness t
• n(soap)=1.42
• n(soap)>n(air) Ray 1 at A
• n(air)<n(soap)Ray 2 at B
• Relative shift ‘
• Ray 2 travels ABC = extra 2t
• “kl2t/n= t/n
• Relative shift “-’= t/n• If m t/n=m or t(m=1)=n/2
– Rays 1 and 2 are out of phase
– Destructive interference
• If m t/n-=m or t(m=0)=n/4
– Rays 1 and 2 are in phase
– Constructive interference
12
film is violet 2t=400nm/2/n t=70nmfilm is red2t=700nm/2/nt=123nm Violet is thinner than red.
B
04/19/23 Lecture VI 12
Diffraction on a single slit
sin22)(zl
z
))((0 Im ztkxie
D
dzEdE
l
x
z
Slit size D, z=-D/2 to D/2Observe diffraction at angle Interference of wavescoming fromdz
04/19/23 Lecture VI 13
Diffraction on a single slit
dzeeD
Edzee
D
EdEE
zitkxizitkxi
sin
2)(0)()(0
sin2)(z
z
l
x
zIntegrate overdz
/sin
)/sinsin(sin
2
sin2)(
0
2/
2/
)(0
D
DeE
zie
Di
EE tkxi
D
D
tkxi e
04/19/23 Lecture VI 14
Diffraction
• Dark spot at
/sin
)/sinsin()(0 D
DeEE tkxi
2
2
0 )/sin(
)/sin(sin/
D
DII
Dm
mD
sin
/sin
1)/sin(
)/sin(sin/
2
2
00 lim
D
DII
• Except =0 – must be bright spot:
04/19/23 Lecture VI 15
Diffraction
• Single slit diffraction• Angular half width of the
first peak:
D
sin