LECTURE LECTURE ONON

INTERFERENCE, DIFFRACTION, INTERFERENCE, DIFFRACTION, POLARISATIONPOLARISATION

BYBY

KAVITA MONGA (LECTURER-PHYSICS)KAVITA MONGA (LECTURER-PHYSICS)

GOVT POLYTECHNIC COLLEGE GOVT POLYTECHNIC COLLEGE KHUNIMAJRA,KHUNIMAJRA,

MOHALIMOHALI

DATE- 14/2/2013DATE- 14/2/2013

TOPICS TO BE COVEREDTOPICS TO BE COVERED

• NATURE OF LIGHT• ELECTROMAGNETIC SPECTRUM• INTERFERENCE• DIFFRACTION• POLARISATION• DIFFERENCE BETWEEN INTERFERENCE &

DIFFRACTION• APPLICATIONS

Light’s Nature

• Wave nature (electromagnetic wave)

• Particle nature (bundles of energy called photons)

Past- Separate Theories of Either Wave or Particle Nature

• Corpuscular theory of Newton (1670) • Light corpuscles have mass and travel at

extremely high speeds in straight lines

• Huygens (1680) • Wavelets-each point on a wavefront acts as a

source for the next wavefront

Proofs of Wave Nature• Thomas Young's Double Slit Experiment (1807) bright (constructive) and dark (destructive) fringes

seen on screen • Thin Film Interference Patterns

• Diffraction fringes seen within and around a small obstacle or through a narrow opening

Proof of Particle Nature:The Photoelectric Effect

• Albert Einstein 1905• Light energy is quantized• Photon is a quantum or packet of energy

The Photoelectric Effect

• Heinrich Hertz first observed the photoelectric effect in 1887

• Einstein explained it in 1905 and won the Nobel prize for this.

Light as waves So far, light has been treated as if it

travels in straight lines.

To describe many optical phenomena, we have to treat light as waves.

Just like waves in water, or sound waves, light waves can interact and form interference patterns. remember c=fλ

2

The Electromagnetic Spectrum

What is the electromagnetic spectrum?

• The energy field created by electricity and magnetism can oscillate and it supports waves that move.

• These waves are called electromagnetic waves.

The Electromagnetic Spectrum

– Electromagnetic waves have both an electric part and a magnetic part and the two parts exchange energy back and forth.–A 3-D view of an

electromagnetic wave shows the electric and magnetic portions.

The Electromagnetic Spectrum

The wavelength and amplitude of the waves are labeled λ and A, respectively.

• The higher the frequency of the light, the higher the energy of the wave.

• Since color is related to energy, there is also a direct relation between color, frequency, and wavelength.

The Electromagnetic Spectrum

Speed of Light

c = f l

Wavelength (m)

Frequency (Hz)

Speed of light3 x 108 m/sec

Calculate wavelength• Calculate the wavelength

in air of blue-green light that has a frequency of 600 × 1012 Hz.

Waves of the electromagnetic spectrum

• Visible light is a small part of the energy range of electromagnetic waves.

• The whole range is called the electromagnetic spectrum and visible light is in the middle of it.

Waves of the electromagnetic spectrum–Radio waves are on the

low-frequency end of the spectrum.–Microwaves range in

length from apprxi. 30 cm (about 12 inches) to about 1 mm.–The infrared (or IR) region

of the electromagnetic spectrum lies between microwaves and visible light.

Waves of the electromagnetic spectrum

–Ultraviolet radiation has a range of wavelengths from 400 down to about 10 nm.–X-rays are high-frequency

waves that have great penetrating power and are used extensively in medical and manufacturing applications.–Gamma rays are

generated in nuclear reactions.

Interference, Diffraction, and Polarization

What are some ways light behaves like a wave?

Interference, Diffraction, and Polarization

• In 1807, Thomas Young (1773-1829) did the most convincing experiment demonstrating that light is a wave.

• A beam of light fell on a pair of parallel, very thin slits in a piece of metal.

• After passing through the slits, the light fell on a screen.

• A pattern of alternating bright and dark bands formed is called an interference pattern.

INTRODUCTION TO INTERFERENCE– When two or more sets of waves pass through the same

medium, they will cross each other. These waves are not aware of the presence of each other. So the effects produced by one wave are independent of the effects due to the other. The behaviour of these two sets of waves is governed by a universal principle known as “ The Principle of Superposition” which states that the net displacement at a point where two different waves are incident in the vector sum of component displacement.

– Any wave motion in which the amplitudes of two waves combine will show Interference.

INTRODUCTION TO INTERFERENCE

• During interference, energy and displacement are redistributed. At some points, displacement and energy become maximum and at other points displacement and energy become minimum.

• This modification in the distribution of light energy got by the superposition of two or more waves is called interference.

• TYPES OF INTERFERENCE• Constructive Interference• Destructive Interference

Water WavesA wave generator sends periodic water waves A wave generator sends periodic water waves into a barrier with a small gap, as shown below.into a barrier with a small gap, as shown below.

A new set of waves is observed emerging from the gap to the wall.A new set of waves is observed emerging from the gap to the wall.

Interference of Water WavesAn An interference patterninterference pattern is set up by water waves is set up by water waves leaving two slits at the same instant.leaving two slits at the same instant.

Interference in spherical waves

maximum of wave minimum of wave r1=r2

r1

r2

positive constructive interference negative constructive interference destructive interference if r2-r1=nλ then constructive interference occurs if r2-r1=(n+½)λ the destructive interference occurs

light as waves

it works the same as water and sound!

Conditions for Interference

• If two waves have a definite phase relationship then they are coherent.

• Otherwise, they are incoherent (ex: two light bulbs).

• For Interference:–The sources must be coherent.–The sources should be monochromatic.

InterferenceCoherence and Monochromatic

• No coherence between two light bulbs

Coherence timeCoherence length

Some later time or distance

coherence - two or more waves that maintain a constant phase relation.

monochromatic - a wave that is composed of a single frequency. Heisenberg uncertainty relation.

For Constructive Interference:

The waves must arrive to the point of study in phase.

So their path difference must be integral multiples of the wavelength:

L= n n=0,1,2,3,………

interference

constructive interference destructive interference

at any point in time one can construct the total amplitude by adding the individual components

For destructive interference:

, the waves must arrive to the point of study out of phase.

So the path difference must be an odd multiple of /2:

L= n m=1/2,3/2,5/2,….

demo: interference

λ λ

+ + λ λ

= =

destructive interference constructive

interference waves ½λ out of phase

waves in phase

Two Waves Interfering

Thomas Young’s Double Slit Interference Experiment

• Showed an interference pattern

• Measured the wavelength of the light

double slit experiment

•the light from the two sources is incoherent (fixed phase with respect to each other •in this case, there is no phase shift between the two sources •the two sources of light must have identical wave lengths

Young’s ExperimentIn In Young’s experiment, Young’s experiment, light from a monochromatic light from a monochromatic source falls on two slits, setting up an source falls on two slits, setting up an interference interference patternpattern analogous to that with water waves. analogous to that with water waves.

Light source S1

S2

The Superposition Principle• The The resultant displacement resultant displacement of two of two

simultaneous waves (simultaneous waves (blueblue and and greengreen) is ) is the algebraic sum of the two the algebraic sum of the two displacements.displacements.

The superposition of two coherent light The superposition of two coherent light waves results in light and dark fringes on a waves results in light and dark fringes on a screen. screen.

• The The compositecomposite wave is shown in wave is shown in yellow.yellow.

Constructive InterferenceConstructive Interference Destructive InterferenceDestructive Interference

Young’s Interference Patterns1

s2

s1

s2

s1

s2

Constructive

Constructive

Bright fringe

Bright fringe

Dark fringe

Destructive

Conditions for Bright FringesBright fringes occur when the difference in path Bright fringes occur when the difference in path p p is an is an integral multiple of one wave length integral multiple of one wave length ..

pp11

pp22

pp33

pp44

Path difference

p = 0, , 2, 3, …

Bright fringes: p = n, n = 0, 1, 2, . . .

Conditions for Dark FringesDark fringes occur when the difference in path Dark fringes occur when the difference in path p p is an is an odd multiple of one-half of a wave length odd multiple of one-half of a wave length ..

pp11

pp22 2

pp33

pp33

2p n

n n = odd= odd

n n = 1,3,5 = 1,3,5 ……

Dark fringes: 1, 3, 5, 7, . . .2

p n n

Analytical Methods for Fringes

x

y

d sin s1

s2

d

p1

p2

Bright fringes: d sin = n, n = 0, 1, 2, 3, . . .

Dark fringes: d sin = n, n = 1, 3, 5, . . .

p = p1 – p2

p = d sin

Path difference Path difference determines light and determines light and dark pattern.dark pattern.

Analytical Methods (Cont.)x

y

d sin s1

s2

d p1

p2

From geometry, we recall that:From geometry, we recall that:

Bright fringes:

, 0, 1, 2, ...dy

n nx

Dark fringes:

, 1, 3, 5...2

dyn n

x

sin tany

x

So that . . .So that . . .

sindy

dx

Example 1: Two slits are 0.08 mm apart, and the screen is 2 m away. How far is the third dark fringe located from the central maximum if light of wavelength 600 nm is used?

xx = 2 m; = 2 m; dd = 0.08 mm = 0.08 mm

= 600 nm; y = ?= 600 nm; y = ?

The The thirdthird dark fringe dark fringe occurs when occurs when n = 5n = 5

x

y

d sin s1

s2

n = 1, 3, 5

Dark fringes:

, 1, 3, 5...2

dyn n

x

d sin d sin = 5( = 5(/2)/2)

5

2

dy

x

5

2

dy

x

Example 1 (Cont.): Two slits are 0.08 mm apart, and the screen is 2 m away. How far is the third dark fringe located from the central maximum if = 600 nm?

xx = 2 m; = 2 m; dd = 0.08 mm = 0.08 mm

= 600 nm; y = ?= 600 nm; y = ?

x

y

d sin s1

s2

n = 1, 3, 5

5

2

dy

x

5

2

dy

x

-9

-3

5 5(600 x 10 m)(2 m)

2 2(0.08 x 10 m)

xy

d

y = 3.75 cmy = 3.75 cm

Note

The interference is different for light of different wavelengths

Question

Two narrow slits are illuminated by a laser with a wavelength of 600 nm. the distance between the two slits is 1 cm. a) At what angle from the beam axis does the 3rd order maximum occur? b) If a screen is put 5 meter away from the slits, what is the distance between the 0th order and 3rd order maximum?

a) use dsinθ=mλ with m=3 θ=sin-1(mλ/d) =sin-1(3x600x10-9/0.01) =0.01030 b) Ym = m λL/d

m=0: y0=0 m=3: y3=3x600x10-9x5/0.01 =9x10-4 m

=0.9 mm

quiz (extra credit)

Two beams of coherent light travel different paths arriving at point P. If constructive interference occurs at point P, the two beams must:

a) travel paths that differ by a whole number of wavelengths

b) travel paths that differ by an odd number of half wavelengths

Diffraction

Wave bends as it passes an obstacle.

Diffraction of LightDiffractionDiffraction is the ability of light waves to bend is the ability of light waves to bend around obstacles placed in their path.around obstacles placed in their path.DiffractionDiffraction is the ability of light waves to bend is the ability of light waves to bend around obstacles placed in their path.around obstacles placed in their path.

Ocean Beach

Water waves easily bend around obstacles, but Water waves easily bend around obstacles, but light light waveswaves also bend, as evidenced by the lack of a sharp also bend, as evidenced by the lack of a sharp shadow on the wall.shadow on the wall.

Fuzzy Shadow

Light rays

Diffraction Grating• What is a diffraction grating?

• What are the two types?

A diffraction grating is a slide with a large number of slits. Usually expressed in the number of slits per mm.

transmission and reflection gratings

The Diffraction GratingA A diffraction grating diffraction grating consists of thousands of parallel consists of thousands of parallel slits etched on glass so that brighter and sharper slits etched on glass so that brighter and sharper patterns can be observed than with Young’s patterns can be observed than with Young’s experiment. Equation is similar.experiment. Equation is similar.

A A diffraction grating diffraction grating consists of thousands of parallel consists of thousands of parallel slits etched on glass so that brighter and sharper slits etched on glass so that brighter and sharper patterns can be observed than with Young’s patterns can be observed than with Young’s experiment. Equation is similar.experiment. Equation is similar.

d sin

d

d sin n

n = 1, 2, 3, …

Diffraction gratings• A diffraction grating is a precise array of tiny

engraved lines, each of which allows light through.• The spectrum produced is a mixture of many

different wavelengths of light.

How a Diffraction Grating WorksWhen you look at a diffracted

light you see:– the light straight ahead as

if the grating were transparent.

– a "central bright spot".– the interference of all

other light waves from many different grooves produces a scattered pattern called a spectrum.

Diffraction Grating

Diffraction Grating• Large number of equally spaced parallel slits.• Equations are same as for double slit interference but

first calculate the d (slit separation) from the grating density, N.

d=1/N , N slits per unit length

dsinnndx

LConstructive (brights) n=0,1,2,3,…..Destructive (darks) n=1/2, 3/2, 5/2,…..

Spectrometer• A spectrometer is a

device that measures the wavelength of light.

• A diffraction grating can be used to make a spectrometer because the wavelength of the light at the first-order bright spot can be expressed in a mathematical relationship.

The Grating Equation

The grating equation:

sin 1, 2, 3, ...d n n

d = slit width (spacing)

= wavelength of light

= angular deviation

n = order of fringe

1st order

2nd order

A compact disk acts as a diffraction grating. The colors and A compact disk acts as a diffraction grating. The colors and intensity of the reflected light depend on the orientation of intensity of the reflected light depend on the orientation of the disc relative to the eye.the disc relative to the eye.

Diffraction through a Narrow Slit Each part of the slit acts as a point source that

interferes with the others. (Based on Huygens Principle)

Pattern of Diffraction of Light through a Narrow Slit

L

wx

Diffraction from Narrow Slit

w sinn n w y

L w: is the width of the slit

Destructive (dark fringes): n=0,1,2,3,….

Diffraction for a Circular Opening

Circular diffractionCircular diffraction

D

The diffraction of light passing through a circular The diffraction of light passing through a circular opening produces circular interference fringes that opening produces circular interference fringes that often blur images. For optical instruments, the often blur images. For optical instruments, the problem increases with larger diameters problem increases with larger diameters DD..

The diffraction of light passing through a circular The diffraction of light passing through a circular opening produces circular interference fringes that opening produces circular interference fringes that often blur images. For optical instruments, the often blur images. For optical instruments, the problem increases with larger diameters problem increases with larger diameters DD..

Example of Diffraction

DIFFERENCE BETWEEN INTERFERENCE AND DIFFRACTION• In the interference phenomenon, the

superposition is due to two separate wavefronts originating from two coherent sources while in the diffraction phenomenon the superposition is due to secondary wavelets originating from different parts of the same wavefront.

• In the interference, the regions of minimum intensity are perfectly dark while in the diffraction, they are not perfectly dark.

DIFFERENCE BETWEEN INTERFERENCE AND DIFFRACTION• The width of the fringes in the interference

phenomenon is normally equal and uniform while in diffraction, the width between the fringes is never equal.

• In the interference phenomenon, all the positions of maxima are of the same intensity, but in the diffraction phenomenon they are of varying intensity.

Polarization

• Polarization is another wave property of light. • The fact that light shows polarization tells us

that light is a transverse wave.

Polarization• Polarization is a

vector. • A wave with

polarization at 45 degrees can be represented as the sum of two waves.

• Each of the component waves has smaller amplitude.

Polarization

We saw that light is really an electromagnetic wave with electric and magnetic field vectors oscillating perpendicular to each other. In general, light is unpolarized, which means that the E-field vector (and thus the B-field vector as long as it is perpendicular to the E- field) could point in any direction

E-vectors could point anywhere: unpolarized

propagation into screen

polarized light

light can be linearly polarized, which means that the E- field only oscillated in one direction (and the B-field perpendicular to that)

The intensity of light is proportional to the square of amplitude of the E-field. I~Emax2

How to polarize?

absorption

reflection scattering

polarization by absorption

certain material (such as polaroid used for sunglasses) only transmit light along a certain ‘transmission’ axis. because only a fraction of the light is transmitted after passing through a polarizer the intensity is reduced. If unpolarized light passes through a polarizer, the intensity is reduced by a factor of 2

polarization by reflection

If unpolarized light is reflected, n1

than the reflected light is partially polarized.

if the angle between the reflected ray and the refracted ray is exactly 900

the reflected n2 light is completely polarized

the above condition is met if for the angle of incidence the equation tanθ=n2/n1

the angle θ=tan-1(n2/n1) is called the Brewster angle

the polarization of the reflected light is (mostly) parallel to the surface of reflection

Polarization by scattering

certain molecules tend to polarize light when struck by it since the electrons in the molecules act as little antennas that can only oscillate in a certain direction

Polarization• A polarizer is a material that selectively

absorbs light depending on polarization.• A polarizer re-emits a fraction of incident light

polarized at an angle to the transmission axis.

Applications of Polarizers• Polarizing sunglasses

are used to reduce the glare of reflected light

• The LCD (liquid crystal diode) screen on a laptop computer uses polarized light to make pictures.

question

horizontal vertical direction of polarization of reflected light

Because of reflection from sunlight of the glass window, the curtain behind the glass is hard to see. If I would wear polaroid sunglasses that allow … polarized light through, I would be able to see the curtain much better. a) horizontally b) vertically

sunglasses

wearing sunglasses will help reducing glare (reflection) from flat surfaces (highway/water)

without with sunglasses

Interference From Single Slit

Pattern ExaggeratedPattern Exaggerated

When monochromatic light strikes a single slit, When monochromatic light strikes a single slit, diffraction from the edges produces an diffraction from the edges produces an interference interference pattern pattern as illustrated.as illustrated.

Relative intensity

The interference results from the fact that not all The interference results from the fact that not all paths of light travel the same distance some paths of light travel the same distance some arrive out of phase.arrive out of phase.

Single Slit Interference Pattern

a/2

aa/2

sin2

a

1

2

4

3

5

Each point inside slit acts Each point inside slit acts as a source. as a source.

For rays 1 and 3 and for 2 For rays 1 and 3 and for 2 and 4:and 4:

sin2

ap

First dark fringe:First dark fringe:

sin2 2

a sin2 2

a

For every ray there is another ray that differs by this path For every ray there is another ray that differs by this path and therefore interferes destructively.and therefore interferes destructively.

Single Slit Interference Pattern

a/2

aa/2

sin2

a

1

2

4

3

5

sin2 2

a

First dark fringe:First dark fringe:

sina

sina

Other dark fringes occur Other dark fringes occur for integral multiples of for integral multiples of this fraction this fraction /a/a..

Example - Monochromatic light shines on a single slit of width 0.45 mm. On a screen 1.5 m away, the first dark

fringe is displaced 2 mm from the central maximum. What is the wavelength of the light?

x = 1.5 m

y

a = 0.35 mm

= ?

sina

sina

ysin tan ; ;

x

y ya

x a x

(0.002 m)(0.00045 m)

1.50 m

= 600 nm

Resolution of ImagesConsider light through a pinhole. As two Consider light through a pinhole. As two objects get closer the interference fringes objects get closer the interference fringes overlap, making it difficult to distinguish overlap, making it difficult to distinguish separate images.separate images.

Consider light through a pinhole. As two Consider light through a pinhole. As two objects get closer the interference fringes objects get closer the interference fringes overlap, making it difficult to distinguish overlap, making it difficult to distinguish separate images.separate images.

d2

Separate images barely seen

d1

Clear image of each object

Resolution Limit

d2

Resolution limitImages are just resolved when Images are just resolved when central maximum of one central maximum of one pattern coincides with first pattern coincides with first dark fringe of the other dark fringe of the other pattern.pattern.

Images are just resolved when Images are just resolved when central maximum of one central maximum of one pattern coincides with first pattern coincides with first dark fringe of the other dark fringe of the other pattern.pattern.

Resolution LimitResolution LimitSeparate imagesSeparate images

Resolving Power of InstrumentsThe resolving power of an instrument is a measure of its ability to produce well-defined separate images.

The resolving power of an instrument is a measure of its ability to produce well-defined separate images.

0 1.22D

0 1.22D

Limiting angle of resolution:Limiting angle of resolution:

For small angles, For small angles, sin sin ,,and the limiting and the limiting angle of resolution for a circular opening is:angle of resolution for a circular opening is:For small angles, For small angles, sin sin ,,and the limiting and the limiting angle of resolution for a circular opening is:angle of resolution for a circular opening is:

Limiting angleLimiting angle

D

Resolution and Distance

Limiting Angle of Resolution: 0

0 1.22s

D p

ssoo

pp

D

Limiting angle Limiting angle oo

Example - The tail lights ( = 632 nm) of an auto are 1.2 m apart and the pupil of the eye is around 2 mm in diameter.

How far away can the tail lights be resolved as separate images?

ssoo

pp

EyeEye

D

Tail lightsTail lights

00 1.22

s

D p

0

1.22

s Dp

-9

(1.2 m)(0.002 m)

1.22(632 x 10 m)p p = 3.11 km

Summary

Bright fringes:

, 0, 1, 2, ...dy

n nx

Dark fringes:

, 1, 3, 5...2

dyn n

x

Young’s Experiment:Young’s Experiment:

Monochromatic light falls on two Monochromatic light falls on two slits, producing interference slits, producing interference fringes on a screen.fringes on a screen.

x

y

d sin s1

s2

d p1

p2

sindy

dx

Summary (Cont.)

The grating equation:

sin 1, 2, 3, ...d n n

d = slit width (spacing)

= wavelength of light

= angular deviation

n = order of fringe

Summary (Cont.)

Pattern ExaggeratedPattern Exaggerated

Relative Intensity

Dark Fringes: sin 1, 2, 3, . . .n na

Dark Fringes: sin 1, 2, 3, . . .n na

Interference from a single slit of width Interference from a single slit of width aa::Interference from a single slit of width Interference from a single slit of width aa::

Summary (cont.)

Limiting Angle of Resolution: 0

0 1.22s

D p

ssoo

pp

D

Limiting angle Limiting angle oo

The resolving power of instruments.The resolving power of instruments.The resolving power of instruments.The resolving power of instruments.

diffraction

In Young’s experiment, two slits were used to produce an interference pattern. However, interference effects can already occur with a single slit.

This is due to diffraction: the capability of light to be “deflected” by edges/small openings.

In fact, every point in the slit opening acts as the source of a new wave front

interference pattern from a single slit

pick two points, 1 and 2, one in the top top half of the slit, one in the bottom half of the slit. Light from these two points interferes destructively if:

Δx=(a/2)sinθ=λ/2 so sinθ=λ/a

we could also have divided up the slit into 4 pieces:

Δx=(a/4)sinθ=λ/2 so sinθ=2λ/a

6 pieces: Δx=(a/6)sinθ=λ/2 so sinθ=3λ/a

Minima occur if sinθ=mλ/a m=1,2,3…

In between the minima, are maxima: sinθ=(m+1/2)λ/a m=1,2,3… AND sinθ=0 or θ=0

slit width

a a

if λ>a sinθ=λ/a > 1 if λ<<a λ<a : interference Not possible, so no sinθ=mλ/a is very small pattern is seen patterns diffraction hardly seen

the diffraction pattern

The intensity is not

uniform: I=I0sin2(β)/β2

β=πa(sinθ)/ λ

a a a a a a

question

light with a wavelength of 500 nm is used to illuminate a slit of 5μm. At which angle is the 5th minimum in the diffraction pattern seen?

sinθ=mλ/a θ=sin-1(5x500x10-9/(5x10-6))=300

diffraction from a single hair

instead of an slit, we can also use an inverse image, for example a hair! demo

double slit interference revisited

The total response from a double slit system is a combination of two single-source slits, combined with a diffraction pattern from each of the slit due to diffraction

minima asinθ=mλ, m=1,2,3… maxima asinθ=(m+1/2)λ, m=1,2,3… and θ=0

a: width of individual slit

due to 2-slit interference

maxima dsinθ=mλ, m=0,1,2,3… minima dsinθ=(m+1/2)λ, m=0,1,2,3… d: distance between two slits

double-slit experiment a

d

if λ>d, each slit acts as a single if λ<d the interference spectrum source of light and we get is folded with the diffraction a more or less prefect double-slit pattern. interference spectrum

question

7th

A person has a double slit plate. He measures the distance between the two slits to be d=1 mm. Next he wants to determine the width of each slit by investigating the interference pattern. He finds that the 7th order interference maximum lines up with the first diffraction minimum and thus vanishes. What is the width of the slits?

7th order interference maximum: dsinθ=7λ so sinθ=7λ/d 1st diffraction minimum: asinθ=1λ so sinθ=λ/a sinθ must be equal for both, so λ/a=7λ/d and a=d/7=1/7 mm

diffraction grating

consider a grating with many slits, each separated by

d a distance d. Assume that for each slit λ>d. We saw that for 2 slits maxima appear if:

dsinθ=mλ, m=0,1,2,3… This condition is not changed for in the case of n slits.

diffraction gratings can be made by scratching lines on glas and are often used to analyze light instead of giving d, one usually gives the number of slits per unit distance: e.g. 300 lines/mm d=1/(300 lines/mm)=0.0033 mm

separating colors

dsinθ=mλ, m=0,1,2,3… for maxima (same as for double slit) so θ=sin-1(mλ/d) depends on λ, the wavelength.

cd’s can act as a diffraction grating

question

If the interference conditions are the same when using a double slit or a diffraction grating with thousands of slits, what is the advantage of using the grating to analyze light?

a) the more slits, the larger the separation between maxima.

b) the more slits, the narrower each of the bright spots and thus easier to see

c) the more slits, the more light reaches each maximum and the maxima are brighter

d) there is no advantage

question

An diffraction grating has 5000 lines per cm. The angle between the central maximum and the fourth order maximum is 47.20. What is the wavelength of the light?

dsinθ=mλ, m=0,1,2,3… d=1/5000=2x10-4 cm=2x10-

6 m m=4, sin(47.2)=0.734 so λ= dsinθ/m=2x10-6x0.734/4=3.67x10-7 m=367 nm

Reading Question

What was the first experiment to show that light is a wave?

1. Young’s double slit experiment2. Galileo’s observation of Jupiter’s moons3. The Michelson-Morley interferometer4. The Pound-Rebka experiment5. Millikan’s oil drop experiment

Reading Question

What was the first experiment to show that light is a wave?

1. Young’s double slit experiment2. Galileo’s observation of Jupiter’s moons3. The Michelson-Morley interferometer4. The Pound-Rebka experiment5. Millikan’s oil drop experiment

Reading QuestionWhat is a diffraction grating?

1. A device used to grate cheese and other materials2. A musical instrument used to direct sound3. A plaque with a tiny circular aperture4. An opaque objects with many closely spaced slits5. Diffraction gratings are not covered in Chapter 22.

Reading QuestionWhat is a diffraction grating?

1. A device used to grate cheese and other materials2. A musical instrument used to direct sound3. A plaque with a tiny circular aperture4. An opaque objects with many closely spaced slits

Reading QuestionWhen laser light shines on a screen after passing through two closely spaced slits, you see

1. a diffraction pattern.2. interference fringes.3. two dim, closely spaced points of light.4. constructive interference.

Reading QuestionWhen laser light shines on a screen after passing through two closely spaced slits, you see

1. a diffraction pattern.2. interference fringes.3. two dim, closely spaced points of light.4. constructive interference.