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Today’s agenda:
Review of Waves.
You are expected to recall facts about waves from Physics 23.
Young’s Double Slit Experiment.
You must understand how the double slit experiment produces an interference pattern.
Conditions for Interference in the Double Slit Experiment.
You must be able to calculate the conditions for constructive and destructive interference
in the double slit experiment.
Intensity in the Double Slit Experiment.
You must be able to calculate intensities in the double slit experiment.
Interference
Review of Waves
This section is a review of material you learned in your
previous physics course (probably Physics 23).
Consider a wave described by
y(x,t) A sin (kx ωt).
The phase of this wave is
θ(x,t) kx ωt.
Also
dθ dx k ω.
dt dt
y
x
When waves of the same nature travel past some point at the
same time, the amplitude at that point is the sum of the
amplitudes of all the waves
The amplitude of the electric field at a point is found by adding
the instantaneous amplitudes, including the phase , of all
electric waves at that point.
In Physics 23 you may have learned that power (or intensity)
is proportional to amplitude squared. The intensity of the
superposed waves is proportional to the square of the
amplitude of the resulting sum of waves.
Superposition—a Characteristic of All Waves
Constructive Interference: If the waves are in phase, they
reinforce to produce a wave of greater amplitude.
Destructive Interference: If the waves are out of phase,
they reinforce to produce a wave of reduced amplitude.
Interference—a Result of the Superposition of Waves
This experiment demonstrates the
wave nature of light.
Consider a single light source, and
two slits. Each slit acts as a
secondary source of light.
Light waves from secondary slits
interfere to produce alternating
maxima and minima in the
intensity.
Reference and “toys:” fsu magnet lab, colorado
light cannon, wave interference, double slit.
Young’s Double Slit Experiment
Interesting reading: the double slit experiment and quantum mechanics.
But don’t take it too literally.
How does this work?
Light waves from the two slits arriving at the detection screen in
phase will interfere constructively and light waves arriving out of
phase will interfere destructively. Another applet (useful).
In phase—
constructive.
Out of phase—
destructive.
Video, with some teasers about quantum mechanics.
Disclaimer! The video ends up heading towards shaky ground.
See, for example, Schrödinger’s Cat:
“One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.”—Erwin Schrödinger
“The idea of a particle existing in a superposition of possible states, while a fact of quantum mechanics, is a concept that does not scale to large systems (like cats), which are not indeterminably probabilistic in nature.”—Wikipedia
Electron double slit applet.
To avoid streaming that video, I’ll play this in class.
Today’s agenda:
Review of Waves.
You are expected to recall facts about waves from Physics 23.
Young’s Double Slit Experiment.
You must understand how the double slit experiment produces an interference pattern.
Conditions for Interference in the Double Slit
Experiment.
You must be able to calculate the conditions for constructive and destructive interference
in the double slit experiment.
Intensity in the Double Slit Experiment.
You must be able to calculate intensities in the double slit experiment.
d L 2
L 1
L = L 2 – L 1 = d sin
For an infinitely distant* screen:
P
S 2
S 1
L
R
y
L 1
L 2
d
tan
y
R
*so that all the angles labeled
are approximately equal
Destructive Interference:
Constructive Interference:
The parameter m is called the order of the interference
fringe. The central bright fringe at = 0 (m = 0) is known
as the zeroth-order maximum. The first maximum on either
side (m = ±1) is called the first-order maximum.
d L 2
L 1
L = L 2 – L 1 = d sin
L d sin m , m=0, 1 , 2...
L d sin m+ m=0 1 2... 2
P
S 2
S 1
L
R
y
L 1
L 2
d
tan
y
R
y R tan R sin
Dark fringes:
This is not a starting
equation!
^ ^
m d sin 2
^
1 y m d 2 R
R 1
y m d 2
Do not use the small-angle
approximation unless it is valid!
Example: a viewing screen is separated from the double-slit
source by 1.2 m. The distance between the two slits is 0.
mm. The second-order bright fringe (m = 2) is 4.5 cm from
the center line. Determine the wavelength of the light.
y R tan R sin
Bright fringes:
m d sin
y m d R
yd
Rm
-2 - 7
4.5 10 m 3.0 10 m 5.6 10 m 560 nm 1.2 m 2
P
S 2
S 1
L
R
y
L 1
L 2
tan
y
R
d
Example: a viewing screen is separated from the double-slit
source by 1.2 m. The distance between the two slits is 0.
mm. The second-order bright fringe (m = 2) is 4.5 cm from
the center line. Find the width of the bright fringes.
Define the bright fringe width to be
the distance between two adjacent
destructive minima.
^ ^
1 y dark m d sin d 2 R
dark
R 1
y m d 2
^
7
dark,m+1 dark,m (^) -
5.6 10 m 1.2 m
y -y 2.2 cm
3.0 10 m
P
S 2
S 1
L
R
y
L 1
L 2
tan
y
R
(^) (^) (^) (^) (^) (^)
dark,m+1 dark,m
R 1 R 1 R y -y m 1 m d 2 d 2 d
d
Today’s agenda:
Review of Waves.
You are expected to recall facts about waves from Physics 23.
Young’s Double Slit Experiment.
You must understand how the double slit experiment produces an interference pattern.
Conditions for Interference in the Double Slit Experiment.
You must be able to calculate the conditions for constructive and destructive interference
in the double slit experiment.
Intensity in the Double Slit Experiment.
You must be able to calculate intensities in the double slit experiment.
