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the combination of two or more waves that results in a single wave
Constructive interference
Bright bands are
Destructive interference
Dark bands are
Occurs when two or more pulses meet at some point & the displacement at that point is the algebraic sum of the individual displacements
When two frequencies are different, they cannot be constantly in or out of phase. Instead , a beat is created by their overlaps.
Beat equation
Fb = abs(f2-f1)
Path Difference
The interference caused by the distance between two sources
Destructive Path difference
d = (n+1/2)lambda
Constructive Path difference
d = n lambda
the bending and spreading of waves, usually around an obstacle
Single Slit
Waves spread out and so their is one wide central maximum. However, waves diffract around the edges creating small minimums nearby
Double Slit
Waves from the two slits diffract creating interference with a bright maximum and multiple minimums on the side. Because they are each technically single slits, the single slit effect also occurs
Young's Double Slit Experiment
Young wanted to prove light was a wave so he passed light through a double slit... It worked
Single Slit Equation
d theta = lambda; where d is the width of the slit and theta is the angle between the central maximum and the first minimum
Double Slit Equation
d sin theta = lambda n; where d is the separation of the slits and theta is the angle between the maximum and the nth minimum.
Thin Film Interference
Light passes through a thin film into a high index of refraction than bounces back off of a lower index of refraction, you get multiple waves. These waves can interfere if the path difference is right.
Hard Reflection
If a wave bounces off of a hard surface, it does a complete phase change
Soft Reflection
If a wave bounces off of a relatively softer surface, it doesn't phase change
Thin Film Constructive Equations
One Phase Change: 2d = (n+1/2)lambda
Thin Film Destructive Equations
One Phase Change: 2d = n lambda
Rayleigh's Criteria
The angular separation at which two sources of light are just resolvable
Rayleigh's equation
Angular separation: theta = s/r
Standing waves
A wave in which no energy is being propagated
The first harmonic;
v = rad(Ft/m/L)
v = 330ms^-1 (speed of sound in air)
Two ended tube
Anti-node to anti-node
Interference Pattern
a regular arrangement of places where wave effects are increased, decreased, or neutralized.
region where waves cancel each other out
out of phase
the crests of one wave overlap the troughs of another to produce regions of zero amplitude
In phase
360 degrees or 2π off → When they overlap
When can interference take place?
only btwn waves of same wavelength
constant phase
What must waves have for interference to be observed?
source of light for which the phase distance is constant
sources of light for which phase distance is not constant
two slits produce series of bright and dark parallel bands
diffraction patterns
passing around an obstacle or bending thru slit and interfering with it
wave fronts interfere with each other
a pattern
What does light diffracted by an obstacle produce?
diffraction grating
aperture with thousands of slits, equal separated
wave nature of light
What is diffraction and instrument resolution limited by?
resolving power
ability of optical instruments to form separate images of two objects that are close together
wavelength and aperture width
what does resolution depend on?
A device that produces a narrow beam of coherent light.
What do lasers do?
transform energy to coherent light
measure distances, DVDs, surgery