class22A.ppt

Chapter 37
Interference and Diffraction

Combination of Waves
In general, when we combine two waves to form a composite wave,
the composite wave is the algebraic sum of the two original waves,
point by point in space [Superposition Principle].
When we add the two waves we need to take into account their:
Direction
Amplitude
Phase
+ =

The combining of two waves to form a composite wave is called:
Interference
The interference is constructive
if the waves reinforce each other.
+ =
Constructive interference
(Waves almost in phase)

The combining of two waves to form a composite wave is called:
Interference
The interference is destructive
if the waves tend to cancel each other.
+ =
(Close to p out of phase)
(Waves almost cancel.)
Destructive interference

Interference of Waves
+ =
Constructive interference
(In phase)
+ =
( p out of phase)
(Waves cancel)
Destructive interference

When light waves travel different paths,
and are then recombined, they interfere.
Each wave has an electric field
whose amplitude goes like:
E(s,t) = E0 sin(ks-t) î
Here s measures the distance
traveled along each wave’s path.
Mirror
1
2
*
+ =
Constructive interference results when light paths differ
by an integer multiple of the wavelength: s = m 

When light waves travel different paths,
and are then recombined, they interfere.
Each wave has an electric field
whose amplitude goes like:
E(s,t) = E0 sin(ks-t) î
Here s measures the distance
traveled along each wave’s path.
Mirror
1
2
*
Destructive interference results when light paths differ
by an odd multiple of a half wavelength: s = (2m+1) /2
+ =

Coherence: Most light will only have interference for small
optical path differences (a few wavelengths), because the
phase is not well defined over a long distance. That’s
because most light comes in many short bursts strung
together.
Incoherent light: (light bulb)
random phase “jumps”

Coherence: Most light will only have interference for small
optical path differences (a few wavelengths), because the
phase is not well defined over a long distance. That’s
because most light comes in many short bursts strung
together.
Incoherent light: (light bulb)
Laser light is an exception: Coherent Light: (laser)
random phase “jumps”

Thin Film Interference
We have all seen the effect of colored reflections
from thin oil films, or from soap bubbles.
Film; e.g. oil on water

Rays reflected off the lower
surface travel a longer
optical path than rays
reflected off upper surface.

Rays reflected off the lower
surface travel a longer
optical path than rays
reflected off upper surface.
If the optical paths differ by
a multiple of , the reflected
waves add.
If the paths cause a phase
difference p, reflected waves
cancel out.

1
t
2
oil on water
optical film on glass
soap bubble
n = 1
n > 1
Ray 1 has a phase change of p upon reflection
Ray 2 travels an extra distance 2t (normal incidence approximation)
Constructive interference: rays 1 and 2 are in phase
 2 t = m n + ½ n  2 n t = (m + ½)  [n = /n]
Destructive interference: rays 1 and 2 are p out of phase
 2 t = m n  2 n t = m 

Thin films work with even low
coherence light, as paths are short
Different wavelengths will tend to add constructively at
different angles, and we see bands of different colors.
When ray 2 is in phase with ray 1, they add up constructively
and we see a bright region.
When ray 2 is p out of phase, the rays interfere destructively.
This is how anti-reflection coatings work.
1
t
2
oil on water
optical film on glass
soap bubble
n = 1
n > 1

Michelson Interferometer
A Michelson interferometer uses a beam splitter to create two
different optical paths. This can be used for optical testing.
What is the output?
Input
Mirrors
Beam-splitter Output

What is the output?
- If the output beams are perfectly aligned, they will
interfere uniformly, giving either a bright or dark
output, depending on their relative phase.
Input
Mirrors
Beam-splitter Output

Input
Output
But usually the beams will be a little misaligned:
Interference of misaligned beams:

But usually, the beams will be a little misaligned:
Interference of misaligned beams: (the lines represent maxima)
Input
Output

Input
Output

Regions of high
intensity
Input
Output

Regions of high
intensity
S
Interference of misaligned beams: (lines = maxima)
Input
Output
“Fringes”

Optical Testing With a
Optical
window to
be tested
Input
Mirrors
Output

If the window distorts the
waves, this will show up
in the interference fringes:
Good window.
Optical
window to
be tested
Input
Mirrors
Output

If the window distorts the
waves, this will show up
in the interference “fringes”:
Good window. Bad window
Optical
window to
be tested
Input
Mirrors
Output

class22A.ppt

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