Physics 214 3: Interference, Diffraction and Polarization Young’s Double-Slit Experiment Intensity...

33
Physics 214 terference, Diffraction and Polariz Young’s Double-Slit Experiment Intensity Distribution of the Double-Slit Interference Pattern Interference in Thin Films Single Slit Diffraction Diffraction Grating Diffraction by Crystals Polarization of Light Waves

Transcript of Physics 214 3: Interference, Diffraction and Polarization Young’s Double-Slit Experiment Intensity...

Page 1: Physics 214 3: Interference, Diffraction and Polarization Young’s Double-Slit Experiment Intensity Distribution of the Double-Slit Interference Pattern.

Physics 214Physics 214

3: Interference, Diffraction and Polarization

• Young’s Double-Slit Experiment• Intensity Distribution of the Double-Slit

Interference Pattern• Interference in Thin Films• Single Slit Diffraction• Diffraction Grating• Diffraction by Crystals• Polarization of Light Waves

Page 2: Physics 214 3: Interference, Diffraction and Polarization Young’s Double-Slit Experiment Intensity Distribution of the Double-Slit Interference Pattern.

Double Slit Experiment

In order to observe interference in light rays, light must be:

• Coherent

• Monochromatic

Superposition Principle must apply

Page 3: Physics 214 3: Interference, Diffraction and Polarization Young’s Double-Slit Experiment Intensity Distribution of the Double-Slit Interference Pattern.

In phase Out of phase

r1

r2

d

d

yq

L

x axis

P; (x=0)

Page 4: Physics 214 3: Interference, Diffraction and Polarization Young’s Double-Slit Experiment Intensity Distribution of the Double-Slit Interference Pattern.

path difference d=r2- r1

sin q =d

dÞ d=dsin q=r2

- r1

We get constructive interference when

d=dsinq =m l , m =0,±1,±2, K

We get destructive interference when

d=dsin q= m +12

æ è ç

ö ø

÷ l

Page 5: Physics 214 3: Interference, Diffraction and Polarization Young’s Double-Slit Experiment Intensity Distribution of the Double-Slit Interference Pattern.

for small q

m l

d= sinq » tanq = y

L\ position of FRINGES

y bright = ml Ld

y dark = m + 12( ) l L

dConsider electric field intensity of

the two interfering light waves at the point P

E1 = E0 sin(kx-wt)

E 2= E 0 sin

f only depends on path difference d

path difference of one wavelength l

c

phase difference of 2 p radians

(kx-wt+f)

Page 6: Physics 214 3: Interference, Diffraction and Polarization Young’s Double-Slit Experiment Intensity Distribution of the Double-Slit Interference Pattern.

path difference of l

2

c

phase difference of p radians

\dl= f

2pÞ

df= l

2p

\ f= 2pl

d= 2pldsinq

i.e. f = f q( )

Page 7: Physics 214 3: Interference, Diffraction and Polarization Young’s Double-Slit Experiment Intensity Distribution of the Double-Slit Interference Pattern.

Electric field magnitude at point P, Ep

Ep=E1

+E2=E0 sin +( )

=2E0cosf

2Amplitude

1 2 4 3 4 sin

f=0,2 p, K Ûconstructive interference

f=p,3p, K Ûdestructive interference

Intensity I of combined wave

I µEp max2

Amplitude squared

(kx-wt) (kx-wt+f)sin

(kx-wt+f/2)

Page 8: Physics 214 3: Interference, Diffraction and Polarization Young’s Double-Slit Experiment Intensity Distribution of the Double-Slit Interference Pattern.

Intensity of an electromagnetic wave is given by

I=Sav=EmaxBmax

2m0

=Emax

2

2m0c=

cBmax2

2m0

=cuav

\ Itot=

4E02 cos 2f

22m0c

=4I0 cos 2f

2= Imax cos 2f

2

\ Itot= Imaxcos 2 pdsinq

l

æ è ç

ö ø

÷

as sinq» yL we obtain

Itot= Imaxcos 2 pd

lLy

æ è ç

ö ø

÷

Page 9: Physics 214 3: Interference, Diffraction and Polarization Young’s Double-Slit Experiment Intensity Distribution of the Double-Slit Interference Pattern.

Interference by Thin Films

air

soap

Get destructive and constructive interference depending on wavelength and position of observer: therefore see

colors at different positions.

white light

1800 phase change

no phase change

air

1

2

Page 10: Physics 214 3: Interference, Diffraction and Polarization Young’s Double-Slit Experiment Intensity Distribution of the Double-Slit Interference Pattern.

If ray 1 is 1800 out phase with ray 2 this

is equivalent to a path difference of l n2

wavelength of light in medium

whose refraction index is n is l n =l

n

é

ë

ê ê ê

ù

û

ú ú ú

if 2t=l n2

rays will recombine in phase, in general

2t= m+ 12

æ è ç

ö ø

÷ l n Û 2nt= m+ 12

æ è ç

ö ø

÷ l , m=0,1,2,3,K

constructive interference

2nt=m l , m=1,2,3,K

destructive interference

Page 11: Physics 214 3: Interference, Diffraction and Polarization Young’s Double-Slit Experiment Intensity Distribution of the Double-Slit Interference Pattern.

Interference by Thin Films

air

oilwater

white light

1800 phase change

1800 phase change

2nt = m l , m =1 ,2, 3, Kconstructive interference

2nt = m + 12

æ è

ö ø l , m = 0, 1 ,2, 3, K

destructive interference

t

Page 12: Physics 214 3: Interference, Diffraction and Polarization Young’s Double-Slit Experiment Intensity Distribution of the Double-Slit Interference Pattern.

Spreading out of light is called DIFFRACTION

This can occur when light passes

through small opening

or around object at sharp edges

Page 13: Physics 214 3: Interference, Diffraction and Polarization Young’s Double-Slit Experiment Intensity Distribution of the Double-Slit Interference Pattern.

• Fraunhofer Diffraction

• Light forms plane waves when

reaching screen

• long distance from source

• by converging lens• Fresnel Diffraction

• Wavefronts are not plane waves• short distance from source

Page 15: Physics 214 3: Interference, Diffraction and Polarization Young’s Double-Slit Experiment Intensity Distribution of the Double-Slit Interference Pattern.

In Fraunhofer Diffraction paths of waves are parallel

wave 1 travels further than wave 3 by amount

= path difference = d =a2

sin q same for waves 2 & 4.

If d =l

2Ûphase shift of p( ) waves cancel through

destructive interference. This is true for any waves

that differ by a2 . \waves from upper half

that destructively interfere with waves from bottom half are at angle

a2

sin qd=

l

2Û sin q

d=

l

aThe argument holds when dividing slit into 4 portions

a4

sin qd=

l

2Û sin q

d= 2 l

a

Þ sin qd= m

l

a; m =±1,K

qd

Page 16: Physics 214 3: Interference, Diffraction and Polarization Young’s Double-Slit Experiment Intensity Distribution of the Double-Slit Interference Pattern.

By using the method of phasors one can

find that the electric field at a point P

on the screen due to radiation from all

points within the slit is given by

Eq = E 0

sinpal

sin q{ }pal

sin q

æ

è

ç ç ç

ö

ø

÷ ÷ ÷

= E 0 sincpal

sin q{ }and thus the intensity of radiation by

Iq = I0 sinc2 pal

sin q{ }Þ minima occur at sinq= m

la

; m = ±1, K

Sinc

Page 17: Physics 214 3: Interference, Diffraction and Polarization Young’s Double-Slit Experiment Intensity Distribution of the Double-Slit Interference Pattern.

sinsincsin

cos

sinsinc

4;sin

cos

22max

201

0max2

max2

adII

aII

IId

II

Page 18: Physics 214 3: Interference, Diffraction and Polarization Young’s Double-Slit Experiment Intensity Distribution of the Double-Slit Interference Pattern.

Fresnel / FraunhoferDiffraction from a Single Slit

Far from

the slit

zClose to the slit

Incident plane wave

Slit

Page 19: Physics 214 3: Interference, Diffraction and Polarization Young’s Double-Slit Experiment Intensity Distribution of the Double-Slit Interference Pattern.

Resolving between closely spaced sources

diffraction pattern for

two separate source points that

can be resolved

sources closer together

that can be justresolved

Sources so close that

they cannot be resolved

Page 20: Physics 214 3: Interference, Diffraction and Polarization Young’s Double-Slit Experiment Intensity Distribution of the Double-Slit Interference Pattern.
Page 21: Physics 214 3: Interference, Diffraction and Polarization Young’s Double-Slit Experiment Intensity Distribution of the Double-Slit Interference Pattern.

•Rayleighs Criterion•when central max. of one image falls on

first min. of other image, the images are said to be just resolved

first min in single slit occurs when

sinq =l

a» q (as l < < a Þ q is small )

so qmin =la

q subtended by 2 sources must be ³ qmin

in order to be resolved

For circular apertures of diameter D

q min = 1 .22lD

Page 23: Physics 214 3: Interference, Diffraction and Polarization Young’s Double-Slit Experiment Intensity Distribution of the Double-Slit Interference Pattern.

If d=m l=d sin q, m=0,±1, K

waves from all slits will be in phase at P

Þ bright line at P; m is order # of diffraction pattern

mth order max. for each l occurs at some specific q

All l’s are seen at m = 0 Û q=0

m=1 Þsin ql =ld

m=2 Þsin ql =2 ld

Page 24: Physics 214 3: Interference, Diffraction and Polarization Young’s Double-Slit Experiment Intensity Distribution of the Double-Slit Interference Pattern.

Resolving power of diffraction grating

R=l ave

l 2 - l 1

=l aveDl

=Resolving power

l 1, l 2 two wavelengths that can be just resolved

l 1 £ l £ l 2; l 1 » l 2

gratings with high resolving power can

distinguish small differences in l

R=Nm; N= # of lines of grating

=resolving power of mth order diffraction

Page 25: Physics 214 3: Interference, Diffraction and Polarization Young’s Double-Slit Experiment Intensity Distribution of the Double-Slit Interference Pattern.

for m=0 all wavelengths are indistinguishable

for m=2 for grating with N=5000R=5000X2=10000

therefore min. wavelength difference that can be resolved for

waves with an average wavelength of 600 nm

is 6x10 -2 nm

Page 26: Physics 214 3: Interference, Diffraction and Polarization Young’s Double-Slit Experiment Intensity Distribution of the Double-Slit Interference Pattern.

Diffraction by Crystals

atomic spacings in crystals are approx. 10 -10 nm and therefore can act as 3D

diffraction grating

condition for constructive interference

2dsin =m, m 1, Braggs Law

d

Page 27: Physics 214 3: Interference, Diffraction and Polarization Young’s Double-Slit Experiment Intensity Distribution of the Double-Slit Interference Pattern.

Polarization

Electromagnetic Radiation is made of oscillating electric and magnetic fields, that are perpendicular to each other and to the direction of propagation of the radiation (Transverse Wave). These fields are proportional to each other in magnitude and are in phase.

E

B

Page 28: Physics 214 3: Interference, Diffraction and Polarization Young’s Double-Slit Experiment Intensity Distribution of the Double-Slit Interference Pattern.

In general radiation is made up of a mixture of such fields, with each wave of

light having different orientation i.e

as the electric vectors are always perpendicular to the magnetic ones we

need only show the electric ones .

Page 29: Physics 214 3: Interference, Diffraction and Polarization Young’s Double-Slit Experiment Intensity Distribution of the Double-Slit Interference Pattern.

• Plane Polarized Light• Electric Field is in only one direction.• Light is Linearly Polarized

• E direction is constant in time• Light is Circularly Polarized

• E rotates • Ex = Ey at all times

• Light is Elliptically Polarized • E rotates • Ex Ey at all times

Page 30: Physics 214 3: Interference, Diffraction and Polarization Young’s Double-Slit Experiment Intensity Distribution of the Double-Slit Interference Pattern.

Producing Polarizationcan produce such light by passing through a polaroid sheet (Diochroic Material) this allows only one orientation of electric field through undiminished and completely absorbs the light with electric fields perpendicular to this direction. In general diminishes the intensity according to I I0 cos2

Malus’s Law

Page 31: Physics 214 3: Interference, Diffraction and Polarization Young’s Double-Slit Experiment Intensity Distribution of the Double-Slit Interference Pattern.

polarized light is also produced by reflection

When light strikes a nonmetallic surface at any angle other than perpendicular, the reflected beam is polarized preferentially in the plane parallel to the surface. (light polarized in plane perpendicular to surface is preferentially absorbed or transmitted).

Page 32: Physics 214 3: Interference, Diffraction and Polarization Young’s Double-Slit Experiment Intensity Distribution of the Double-Slit Interference Pattern.

Why is the Sky Blue and daylight polarized?

• Higher frequencies are scattered more than lower ones (refracted more) by the oxygen and nitrogen molecules

• All the visible frequencies are scattered the same by larger objects e.g. water droplets in clouds.

• Scattered light is polarized.

Polarization by Scattering

Page 33: Physics 214 3: Interference, Diffraction and Polarization Young’s Double-Slit Experiment Intensity Distribution of the Double-Slit Interference Pattern.

Polarization by Double Refraction

•Materials that have two indices of refraction depending on the direction of incident rays are called Double Refracting or Birefringent

•These materials produce polarized light