26 Interference & Diffraction
--Physical/Wave Optics
Thin film interference
Interference & Coherent Sources
Superposition & Interference
Superposition: The net response at a
given place and time caused by two or
more stimuli is the sum of the responses
which would have been caused by each
stimulus individually (wikipedia)
Key factor: phase.
Double Slits Interference-1
Fringes
1
r2  r1  (m  )
2
( m  0,1,2,...) ( m  0,1,2,...)
r2  r1  m
Double Slits Interference-2
r2  r1  d sin 
d sin   m
Constructive
1
d sin   (m  )
2
Destructive
( m  0,1,2,...)
y
i f R  d , sin   t an 
R
m
ym  R
d
Constructive
Mirror Equation
(m  1 / 2)
d
Destructive
ym  R
( m  0,1,2,...)
Example: Determining 
m
d
Constructive
( m  0,1,2,...)
ym  R
Interference in Thin Film
2t  m
Constructive
1
2t  (m  )
2
Destructive
( m  0,1,2,...)
Note: when nb > na, reflected wave
undergoes an additional half cycle
(i.e., /2) phase shift.
Example: Interference Fringes
(note: additional /2 phase shift from the bottom reflection)
2t  m
 Destructive
( m  0,1,2,...)
Newton Rings & Applications
Non-reflective & Reflective Coatings
Diffraction & Geometric Optics
Diffraction—Reality
Fresnel diffraction:
Fraunhofer diffraction:
near-field diffraction
far-field diffraction
Single Slit Diffraction
Fresnel & Fraunhofer: Single Slit
Huygens’s Principle:
Every point of a wave front may
be considered the source of
secondary wavelets that spread
out in all directions with a speed
equal to the speed of
propagation of the waves.
Dark Fringes
R
ma
sin   
2
( m  1,2,3,...)
Norm al l y, i s ve ry sm al l sin
,   t an 
m
a
( m  1,2,3,...)
ym  R
y
R
Multiple Slits & Diffraction Gratings
Constructive interference or
bright fringes occur:
d sin   m
( m  0,1,2,3,...)
Destructive interference or
dark fringes occur:
d sin   (m  1 / 2)
( m  0  1,2,3,...)
X-Ray Diffraction
Circular Apertures & Resolving Power
First Dark Ring occurs
sin 1  1.22

D
Resolving Power
Rayleigh’s Criterion (increase D or reduce
 could improve the resolution)
sin 1     res  1.22

D
Holography
Summary: Superposition,
interference, & Coherent Sources
Summary: Double Slits Interference
Summary: Thin Film Interference
Summary: Diffraction & Gratings
Summary: X-Ray Diffraction
Summary: Circular Apertures &
Resolving Power
sin 1  1.22

D
Summary: Holography
Ch 26 Homework
Answers to multiple choice problems
Problems: 1, 6, 11, 15, 25, 27, 47