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

1

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)

2

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

4

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

5

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

6

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#

$

%

& '

(

) *

11

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

13

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

14

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

17