Optics: Reflection, Refraction
05/25/2006
For Interference to Occur
Wave Optics
The wave nature of light is needed to explain various
phenomena
Interference
Diffraction
Polarization
The particle nature of light was the basis for ray
(geometric) optics
Interference
Light waves interfere with each other much like
mechanical waves do
All interference associated with light waves arises
when the electromagnetic fields that constitute the
individual waves combine
Fringe Pattern
The fringe pattern formed
from a Young’s Double
Slit Experiment would
look like this
The bright areas
represent constructive
interference
The dark areas represent
destructive interference
They must maintain a constant phase with respect
to each other-wave go up and down together in
time
Young’s Double Slit Experiment
The waves must have identical wavelengths
Thomas Young first demonstrated interference
in light waves from two sources in 1801
Light is incident on a screen with a narrow slit,
So
The light waves emerging from this slit arrive
at a second screen that contains two narrow,
parallel slits, S1 and S2
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Constructive interference
occurs at the center point
The two waves travel the
same distance
Therefore, they arrive
in phase-a bright fringe
The upper wave travels onehalf of a wavelength farther
than the lower wave
The trough of the bottom
wave overlaps the crest of the
upper wave
This is destructive interference
A dark fringe occurs
Thomas Young first
demonstrated interference
in light waves from two
sources in 1801
Light is incident on a
screen with a narrow slit,
So
The light waves emerging
from this slit arrive at a
second screen that
contains two narrow,
parallel slits, S1 and S2
Bright bands
Interference Patterns
Lecture 16
The sources must be coherent
The upper wave has to travel farther than the lower
wave
The upper wave travels one wavelength farther
Therefore, the waves arrive in phase
Bright fringes occur when the path length differs by
exactly mλ
Optics: Reflection, Refraction
The path
difference,
Understanding
δ, is found from the
beige triangle
δ = r2 – r1 = d sin θ
05/25/2006
the Fringe Pattern
Light and Dark Fringes
This assumes the
paths are parallel
Not exactly parallel,
but a very good
approximation since
L is much greater
than d
Three right Triangles!
Definition of sin θ = δ/d
Or
d sin θ = δ
Definition of tan θ = y/L
For small θ: tan θ = sin θ
Lecture 16
Ө
Bright fringe, produced by constructive interference,
path difference must be either zero or some integral
multiple of the wavelength λ
δ = d sin θbright = m λ
m = 0, ±1, ±2, …
When destructive interference occurs, a dark fringe is
observed
This needs a path difference of an odd half wavelength
δ = d sin θdark = (m + ½) λ
m = 0, ±1, ±2, …
Position of Fringes
d
The positions of the fringes can be measured
vertically from the zeroth order maximum
y = L tan θ ≈ L sin θ
Assumptions: L>>d and d>>λ
Approximation
θ is small so tan θ ≈ sin θ
For bright fringes
ybright =
For dark fringes
ydark =
δ
λL
λL 
d
m
1
m+ 
d 
2
m = 0, ± 1, ± 2 K
m = 0, ± 1, ± 2 K