Optics: Reflection, Refraction
5
4
3
2
1
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
Individual Score

http://quantummechanics.ucsd.edu/ph130a/130_notes/node68.html




Thomas Young first demonstrated interference in light waves from two sources in 1801
Light is incident on a
S screen with a narrow slit, o
The light waves emerging from this slit arrive at a second screen that contains two narrow, parallel slits, S
1 and S
2
05/25/2006


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


The sources must be coherent

They must maintain a constant phase with respect to each other-wave go up and down together in time
The waves must have identical wavelengths

Thomas Young first demonstrated interference in light waves from two sources in 1801
Quick Quiz
• Why is a single wave used to illuminate the two slits in the experiment, producing the interference pattern?
• A. Light sources are expensive and difficult to hook up
• B. It is a good way of producing two waves with the same frequency, amplitude, and phase
• C. Some things don’t matter
• D. Light is a particle, not a wave
Lecture 16

Optics: Reflection, Refraction



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 http://h2physics.org/?cat=48
05/25/2006


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 m λ
Quick Quiz
What is the difference in path lengths for the dark bands?
A.m
λ
B.(m+1) λ
C.(m+½) λ
D.(m+¾) λ
E.Can not be predicted
Light and Dark Fringes





Bright fringe, produced by constructive interference, path difference must be either zero or some integral multiple of the wavelength λ
δ = d sin θ bright

= m m = 0, ± 1, ± 2, …
λ
When destructive interference occurs, a dark fringe is observed
This needs a path difference of an odd half wavelength
δ = d sin θ dark

= (m + ½) m = 0, ± 1, ± 2, …
λ


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
Lecture 16


Understanding the Fringe Pattern
δ , is found from the beige triangle
δ

= r
2
– r
1
= d sin
This assumes the
θ 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 d
Ө
δ




Position of Fringes
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 y bright

 L d m m  0, 1, 2 

For dark fringes y dark

 L  d m 
1
2

 m  0, 1, 2


Optics: Reflection, Refraction


Young’s Double Slit Experiment provides a method for measuring wavelength of the light
This experiment gave the wave model of light a great deal of credibility

It is inconceivable that particles of light could cancel each other
Lecture 16
05/25/2006