Lecture 38
Chapter 36 & 37
Interference & Diffraction
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Interference and Diffraction: Phase Differences and Path Lengths, Study notes of Geology
A lecture on the topics of interference and diffraction of light waves. It covers the three ways phase difference between two waves can change: through media of different indexes of refraction, through different path lengths, and through reflection. The document also discusses the effects of these phase differences on interference, including constructive and destructive interference, and the relationship between path length difference and angle with the central axis. Additionally, the document touches on reflection phase shifts and phase shifts from thin films.
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Lecture 38Chapter 36 & 37
Interference & Diffraction
Review
ï^
3 ways for phasedifference between 2light waves to changeñ Waves travel through
media of differentindexes of refraction,
n
ñ Waves travel along
paths of different lengths ñ Waves are reflected
Review
ï^
Materials of different nñ Different
#
ís of wavelengths
occur in different nís ñ Phase shift given byñ Effective phase difference is
decimal fraction ñ 1
λ
= 2
π
radians = 360∞
)
(^
1
2
1
2
n
n L
N
N
−
=
−
λ
ñ Central maximum at m=0, first order maxima m=1,
second order maxima m= ñ Waves interfere fully destructively whenñ First order minima m=0, second order minima m=1,
third order minima m=
Review
ï^
Different path lengthsñ Ray 1 travels distance
∆
L
farther than ray 2 ñ Waves interfere fully
constructively when
0,1,2,...
,^
=
=
∆
m
m
L
λ
0,1,2,...
, ) 2 1
(^
=
=
∆
m
m
L
λ
Review
ï^
Different path lengths ï^
Use small angle relation ï^
Distance
y
on screen from
central maxima to maximaof order m isñ
D
is distance between screen and slits,
d
is
distance between slits
sin
tan
d
mD
y
Review
ï^
Reflection ï^
If incident light reflected bysurface with lower
n
no
phase shiftñ n1 > n2, phase shift = 0 ï^
If incident light reflected bysurface with higher
n
phase
shifted by Ω
λ
ñ n1 < n2, phase shift = 0.
λ
ï^
Refracted light is not phase shifted
Review
ï^
Checkpoint #5 ñ Light reflects
from film of
thickness L between 2 other media. For givenindex of refractions, which situations will A) givezero phase difference from reflection at filminterfaces
If n1>n2, no phase changeIf n1<n2, Ω
λ
phase change
Review
ï^
(1) n1>n2>n3 ñ no phase shift either surface,phase diff = 0, in phase ï^
(2) n1>n2<n3 ñ top surface no phase shift,bottom surface shifted Ω
λ
, phase diff = Ω
λ
ï^
(3) n1>n2<n3 ñ same as (2) phase diff = Ω
λ
ï^
(4) n1<n2<n3 ñ top and bottom surface bothhave Ω
λ
phase shift, phase diff = 0, in phase
Diffraction (1)
ï^
Waves diffract (bend) if pass through an openingwhose size is comparable to its wavelength ï^
The narrower the slit, the greater the diffraction ï^
Previous example of double-slit interferenceassumed slit width
a
much smaller than
λ
of
incident light and we talked about 2 light rays
Diffraction (2)
ï^
Do we still get aninterference pattern if wehave only one slit? ï^
Yes, see a bright centralmaximum and then otherless bright spots on thesides (side maxima)separated by dark minimañ Caused by interference of
wavelets from samewavefront going through slit