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Physics 104

Lecture 12

Electromagnetic Waves(Interference & Diffraction)

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Communiversity

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Princeton Nursery SchoolMay 5th

Liberty Science CenterMay 11th

Foundation AcademyMay 12th

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Final Exam Announcement

Friday, May 16th

1:30pm-4:30pm

McDonnell A01, A02 and Jadwin A10

Closed book, Closed notes No calculators or electronic devices

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Remember:

Exam 4 is a take-home (45min.)available onlinestarting at noon on Friday May 2nd.

Due by NEXT Friday May 9that noonuse the

PHY 104 return box in Jadwin Hall on the 1st Floor

near the Entrance

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Superposition Principle

Superposition principle states that the

total electric or magnetic field due to two

sources is the sum of the individual

fields:

EM waves consist of propagating E andB fields.

The E and B fields of two sources add

according to the superposition principle.

E total = E1 + E2 +...

Btotal =

B1 +

B2 +...

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Interfering waves withunequal amplitudes: EB=.9EA

ConstructiveA and B in phase Wave A

Wave B

Wave A+B

DestructiveA and B outof phase 1/2

cycle (180o)

Wave A

Wave B

Wave A+B

t

t

E

E

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Coherence

Two or more waves can produce interference effects.

To get a consistent interference effect, the two

waves must be coherent.

Coherent means that the phase difference between the

waves is constant.

Two incandescent light bulbs do not produce coherent

waves, since the light in each is produced by atoms

radiating independently and randomly.6

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Question

150 nm

nm600=

Q1. Is the interference between

the reflected beams:

A) Constructive

B) Destructive

C) Somewhere in between

D) Not enough information

given.

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Producing coherenceand phase shifts.

Single light source,

split into two beams.

Single light source,reflected off two surfaces.

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Speed of light intransparent media v = c/n

Speed of light in vacuum = c = 0f0

Speed of light in media is less than c:

vc

n

c

n index of refraction : n > 1

vc

n0f0

nf

But frequency depends on the oscillating charthat produced the EM wave.

f f0

0n 9

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Phase shift due to reflections

Reflections can produce phase shifts:

1) Reflection from less dense medium off more densemedium (hard reflection):

phase shift is equivalent to /

2) Reflections from more dense medium off less dense

medium (soft reflection):

phase shift is 0

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Thin film interference

Example:

n1

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Q2. What is condition fordestructive interference?

n1< n2> n3

Ray 1 has phase shift of /.

Ray 2 has no phase shift.

(A) 2 twater = 0,

2 twater = / / water= /n

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Thi Fil I f i

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Thin-Film Interference insoap bubble

Gravity makes the

bubble thin at the top

and thick at the bottom.

Why is it black at the

top?

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Phasing in an Antenna Array

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Huygens Principle

Each point on a

primary waveform

serves as the sourceof spherical

secondary wavelets

that advance with a

speed and frequencyequal to those of the

primary wave.

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2-slit interference waterwaves

By passing water waves

through narrow slits,

one generates sphericalwavelets emanating

from each slit.

The two wavelets then

interfere.

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Interference-path difference

Path length differences

are a common source of

phase shifts.

Phase difference: 2 r

wherer = path difference

and= wavelength 17

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Interference fromTwo (Very Narrow) Slits

md =sin

)(sin2

1+= md

Interference maxima:

Interference minima:18

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Microwave zone plate

In this demo you see vividly how microwaves can

interfere, depending on their path difference.

Each zone plate corresponds to a different path length

from the source to the detector.

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Microwave zone plate demo

The zone plate with some

of the zones removed.The microwave detector is

shown in front of the plate.

The source is behind the plate.

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Zone plate

Source Detector

L1L1

L2 L2

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Zone plate condition forinterference

Source Detector

L1 L1L2 L2

Constructive: 2L1-2L2=

Destructive: 2L1- 2L2= /

/

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Single Slit Diffraction

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Pin Hole Camera (Airy Spot)

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Point

Source

Pin

Hole

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What about a solidsphere?

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Q3. What will happen if we shine laser light

at a solid sphere?

a) Will create a solid black shadow

b) Some light will appear on the screen directly

on the axis of the laser beam

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Poisson Point

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Point

Source

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Poisson Point

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Single Slit Diffraction

L

y=tan

=sina

But since

sintan

a

Ly

=

The narrower the slit,

the wider the diffraction

pattern.

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D bl lit I t f

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Double-slit Interferencewith Diffraction

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In general, one observes the combined effects of two-slit

and single-slit interference. Here d = 5a.

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Diffraction Grating (N slits)

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Atomic Line Spectra

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Single Photon Counting

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3000 photons 10,000 photons

100,000 photons 1M photons

4 M photons 30 M photons

How aboutInterference?