InterferenceInterference

Light waves interfere with each Light waves interfere with each other much like mechanical waves other much like mechanical waves dodo

All interference associated with All interference associated with light waves arises when the light waves arises when the electromagnetic fields that electromagnetic fields that constitute the individual waves constitute the individual waves combinecombine

Conditions for InterferenceConditions for Interference

For sustained interference between For sustained interference between two sources of light to be observed, two sources of light to be observed, there are two conditions which there are two conditions which must be metmust be met The sources must be The sources must be coherentcoherent

They must maintain a constant phase with They must maintain a constant phase with respect to each otherrespect to each other

The waves must have identical The waves must have identical wavelengthswavelengths

D

Conditions for InterferenceConditions for InterferenceD>>d>> a<

screen

a

Producing Coherent Producing Coherent SourcesSources

Light from a monochromatic source is Light from a monochromatic source is allowed to pass through a narrow slitallowed to pass through a narrow slit

The light from the single slit is allowed The light from the single slit is allowed to fall on a screen containing two to fall on a screen containing two narrow slitsnarrow slits

The first slit is needed to insure the light The first slit is needed to insure the light comes from a tiny region of the source comes from a tiny region of the source which is coherentwhich is coherent

Old methodOld method

Producing Coherent Producing Coherent Sources, contSources, cont

Currently, it is much more common Currently, it is much more common to use a laser as a coherent sourceto use a laser as a coherent source

The laser produces an intense, The laser produces an intense, coherent, monochromatic beam coherent, monochromatic beam over a width of several millimetersover a width of several millimeters

Young’s Double Slit Young’s Double Slit ExperimentExperiment

Thomas Young first demonstrated Thomas Young first demonstrated interference in light waves from two interference in light waves from two sources in 1801sources in 1801

Light is incident on a screen with a Light is incident on a screen with a narrow slit, Snarrow slit, Soo

The light waves emerging from this The light waves emerging from this slit arrive at a second screen that slit arrive at a second screen that contains two narrow, parallel slits, contains two narrow, parallel slits, SS11 and S and S22

Young’s Double Slit Young’s Double Slit Experiment, DiagramExperiment, Diagram

The narrow slits, SThe narrow slits, S11 and Sand S2 2 act as act as sources of wavessources of waves

The waves The waves emerging from the emerging from the slits originate from slits originate from the same wave the same wave front and therefore front and therefore are always in phaseare always in phase

Resulting Interference Resulting Interference PatternPattern

The light from the two slits form a The light from the two slits form a visible pattern on a screenvisible pattern on a screen

The pattern consists of a series of bright The pattern consists of a series of bright and dark parallel bands called and dark parallel bands called fringesfringes

Constructive interferenceConstructive interference occurs where occurs where a bright fringe occursa bright fringe occurs

Destructive interferenceDestructive interference results in a results in a dark fringedark fringe

Interference PatternsInterference Patterns

Constructive Constructive interference interference occurs at the occurs at the center pointcenter point

The two waves The two waves travel the same travel the same distancedistance Therefore, they Therefore, they

arrive in phasearrive in phase

Interference Patterns, 2Interference Patterns, 2 The upper wave has The upper wave has

to travel farther to travel farther than the lower wavethan the lower wave

The upper wave The upper wave travels one travels one wavelength fartherwavelength farther Therefore, the waves Therefore, the waves

arrive in phasearrive in phase A bright fringe A bright fringe

occursoccurs

Interference Patterns, 3Interference Patterns, 3

The upper wave The upper wave travels one-half of a travels one-half of a wavelength farther wavelength farther than the lower wavethan the lower wave

The trough of the The trough of the bottom wave bottom wave overlaps the crest of overlaps the crest of the upper wavethe upper wave

This is destructive This is destructive interferenceinterference A dark fringe occursA dark fringe occurs

Interference EquationsInterference Equations

The path The path difference, difference, δ, is δ, is found from the tan found from the tan triangletriangle

δ = rδ = r22 – r – r11 = d sin θ = d sin θ This assumes the This assumes the

paths are parallelpaths are parallel Not exactly, but a Not exactly, but a

very good very good approximationapproximation

Interference Equations, 2Interference Equations, 2

For a bright fringe, produced by For a bright fringe, produced by constructive interference, the path constructive interference, the path difference must be either zero or some difference must be either zero or some integral multiple of of the wavelengthintegral multiple of of the wavelength

δ = d sin θδ = d sin θbrightbright = m λ = m λ m = 0, ±1, ±2, … m = 0, ±1, ±2, … m is called the m is called the order numberorder number

When m = 0, it is the zeroth order maximumWhen m = 0, it is the zeroth order maximum When m = ±1, it is called the first order maximumWhen m = ±1, it is called the first order maximum

Interference Equations, 3Interference Equations, 3

When destructive interference When destructive interference occurs, a dark fringe is observedoccurs, a dark fringe is observed

This needs a path difference of an This needs a path difference of an odd half wavelengthodd half wavelength

δ = d sin θδ = d sin θdarkdark = (m + ½) λ = (m + ½) λ m = 0, ±1, ±2, … m = 0, ±1, ±2, …

Interference Equations, 4Interference Equations, 4

The positions of the fringes can be The positions of the fringes can be measured vertically from the zeroth measured vertically from the zeroth order maximumorder maximum

y = L tan y = L tan θ ~ θ ~ L sin L sin θθ AssumptionsAssumptions

L>>dL>>d d>>λd>>λ

ApproximationApproximation θ is small and therefore the approximation θ is small and therefore the approximation

tan tan θ ~ θ ~ sin sin θ can be usedθ can be used

Interference Equations, Interference Equations, finalfinal

For bright fringesFor bright fringes

For dark fringesFor dark fringes

2,1,0mmd

Lybright

2,1,0m2

1m

d

Lydark

Uses for Young’s Double Uses for Young’s Double Slit ExperimentSlit Experiment

Young’s Double Slit Experiment Young’s Double Slit Experiment provides a method for measuring provides a method for measuring wavelength of the lightwavelength of the light

This experiment gave the wave This experiment gave the wave model of light a great deal of model of light a great deal of credibilitycredibility It is inconceivable that particles of It is inconceivable that particles of

light could cancel each otherlight could cancel each other