Reminder: Light and Optics
Physics 202, Lecture 27
" Nature of Lights
#  Lights as rays
#  Lights as EM waves: f, !, ", v, A, interference …
#  Lights as group of photons
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
" 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)
1
Ray Approximation
Huygens’ Principle
"  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
2
" 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
3
4
Reminder: Light Waves
Interference of 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.
E
B
"  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)
$"=" -"
1
% E=E1+E2 = 2E0 cos($"/2) sin(#t+ "/2)
% Resulting amplitude: Emax= 2E0cos($"/2)
#  Constructive interference: $"=0, 2%, 4%,… Emax=2E0
#  Destructive interference: $"=%, 3%, 5%,… Emax=0
y
c
z
x
5
Test of the Wave Nature of Light:
Double-Slit Experiment
" Rays or Waves:
If lights behave as rays
2
"="1+"2
Diffraction & interference
Q: If the intensity of each incoming light is &, what is the
resulting intensity when (1):constructive, (2):destructive?6
Young’s Famous Double-Slit Experiment
Thomas Young (1803)
$  See demo
If lights behave as waves
7
8
Double-Slit Experiment Explained
Double-Slit Experiment Explained
" The experiment can be easily explained by interference
Constructive, $"=0%, 2%, 4%,..'
" The experiment can be easily explained by interference
Constructive, $"=0%, 2%, 4%,..'
Destructive, $"=%, 3%, 5%,..'
Destructive, $"=%, 3%, 5%,..'
9
10
Two-slit interference, quantitatively
Two-Slit Experiment: Summary
$  Constructive: $" =0%, 2%, 4%,…, or 2m%, m=0,1,2…
2"d
sin $ = 2m"
#
path length difference
( =dsin) ~ d) ~ d y/L
Bright spots
!
"# = k(r2 $ r1 ) = kd sin % =
d sin " = m#
$  Destructive: $" =%, 3%, 5%,…, or (2m+1) %, m=0,1,2… '
!
2"d
sin $ = 2(m + 1)"
#
2&d
2 % "d sin # (
*
sin % I = Io cos '
& $ 11)
'
1
d sin " = (m + ) #
2
Dark spots
!
12
Possible Phase Change of 180o
For Reflected Light
Thin Film Interference
" 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:
phase shift
180o(%)
0o
n1>n2:
phase shift
13
Thin Film Interference
Exercise: Non Reflective Coating
" Thin film splits light ! split lights then interfere
lights 1,2 interfere
n!!n=!/n
lights 3,4 also interfere
14
phase change %'
for light 1
" Determine the minimum thickness (t) of SiO coating
so a light of 550nm is non-reflective at the surface.
$"12 ~ 2%/!n (2t) + %'
Solution (see board):
Non “reflective”
!1 and 2 cancel each other
(destructive interference)
Quiz:
Constructive/destructive
Conditions?
$"12 = (2%/!n)(2t) + 0o = %'
t
% t= !n/4 = !/4n = 94.8 nm.
Note t depends on !.
$"34 ~ 2%/!n (2t) '
15
16
Newton’s Rings
Demos
Testing glass for
flatness
17