Post on 17-Jan-2020
Physics 202, Lecture 27 Today’s Topics
! Wave Nature of Waves: Interference ! Breakdown of ray approximation ! Huygen’s principle ! Light as Waves ! Two-Slit Interference
! Thin Film Interference ! Change of Phase at Boundaries ! Exercise on Thin Film Interference ! Exercise on Non Reflective Coating
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Reminder: Light and Optics " Nature of Lights
# Lights as rays # Lights as EM waves: f, !, ", v, A, interference … # Lights as group of photons
" Optics: Physics of lights # Geometric Optics: Treat light as rays (Ch. 31,32) ! Ray approximation.
# Wave Optics: Wave properties becomes important Interference, diffraction…(Ch. 33,34)
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Ray Approximation " When the wavelength of the light is much smaller than
the size of the optical objects it encounters, it can be treated as (colored) rays.
Ray approximation is valid when !<<d
Ray approximation is not valid near the gap when !~d. OK elsewhere 3
Huygens’ Principle " Every point on a wave front can be considered as a
secondary source of waves that spread out in the forward direction. The new wave is the result of the superposition of these secondary waves
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Reminder: Light Waves " Nature of Lights: Rays (classical), "EM waves#, "Photons#. " Review: Electromagnetic plane waves
E= Emaxsin(#t-kx+"), B= Bmaxsin(#t-kx+"), E/B=c $ The E component and B component of an EM wave
are 100% correlated, so we can use just one of them to represent an EM wave.
x
y
z
E
B c
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Interference of Light Waves
" When two light waves meet at certain location, the resulting effect is determined by the superposition ( i.e. sum) of the two individual waves
$ e.g. Two light waves with same color and amplitude. E1= E0sin(#t-kx+"10) = E0sin(#t+"1) E2= E0sin(#t-kx+"20) = E0sin(#t+"2)
% E=E1+E2 = 2E0 cos($"/2) sin(#t+ "/2) % Resulting amplitude: Emax= 2E0cos($"/2)
# Constructive interference: $"=0, 2%, 4%,… Emax=2E0 # Destructive interference: $"=%, 3%, 5%,… Emax=0
Q: If the intensity of each incoming light is &, what is the resulting intensity when (1):constructive, (2):destructive?
$"="1-"2 "="1+"2
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Test of the Wave Nature of Light: Double-Slit Experiment
" Rays or Waves:
If lights behave as rays If lights behave as waves
Diffraction & interference
7
Young’s Famous Double-Slit Experiment Thomas Young (1803)
$ See demo 8
Double-Slit Experiment Explained " The experiment can be easily explained by interference
Constructive, $"=0%, 2%, 4%,..' Destructive, $"=%, 3%, 5%,..'9
Double-Slit Experiment Explained " The experiment can be easily explained by interference
Constructive, $"=0%, 2%, 4%,..' Destructive, $"=%, 3%, 5%,..'10
Two-slit interference, quantitatively
path length difference ( =dsin) ~ d) ~ d y/L
!
"# = k(r2 $ r1) = kd sin% =2&d'
sin%
!
I = Io cos2 "d sin#
$
%
& '
(
) *
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Two-Slit Experiment: Summary
$ Constructive: $" =0%, 2%, 4%,…, or 2m%, m=0,1,2…
$ Destructive: $" =%, 3%, 5%,…, or (2m+1) %, m=0,1,2… '!
2"d#sin$ = 2m"
!
d sin" = m#
!
2"d#sin$ = 2(m +1)"
!
d sin" = (m +12)#
Bright spots
Dark spots 12
Thin Film Interference
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Possible Phase Change of 180o For Reflected Light
" When a light traveling in medium 1 of n1 is reaches at a boundary with medium 2 of n2: # The reflected light has a 180o(%) phase shift if n1<n2 # There is no phase change for reflected light if n1>n2
# In any change, no phase shift for refracted light n1<n2:
180o(%) phase shift n1>n2:
0o phase shift
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Thin Film Interference " Thin film splits light ! split lights then interfere
lights 3,4 also interfere
lights 1,2 interfere lights 1,2 interfere
n!!n=!/n
$"12 ~ 2%/!n (2t) + %'
phase change %'for light 1
$"34 ~ 2%/!n (2t) '
Quiz: Constructive/destructive
Conditions?
15
Exercise: Non Reflective Coating " Determine the minimum thickness (t) of SiO coating
so a light of 550nm is non-reflective at the surface.
t
Solution (see board): Non “reflective” !1 and 2 cancel each other (destructive interference)
$"12 = (2%/!n)(2t) + 0o = %'
% t= !n/4 = !/4n = 94.8 nm.
Note t depends on !.
16
Demos Newton’s Rings Testing glass for flatness
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