Wave Interference and Wave Interference and DiffractionDiffraction

Diffraction of LightDiffraction of Light

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

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

Ocean Beach

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

Fuzzy Shadow

Light rays

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

Figure 2 on p. 459- Figure 2 on p. 459- both waves both waves encounter same obstacle (blue object)encounter same obstacle (blue object)

Figure 2A Figure 2B

- Short wavelengths- Less diffraction (red

arrows)

- Longer wavelengths- Greater amount of

diffraction (red arrows)

Figure 3 on p. 460- all 3 diagrams have the same slit opening. The wavelength increases from a-c, so does the amount of diffraction

Figure 4 on p. 460- Fig 4a and b have a wave with the same wavelength, however slit opening decreases. As slit width decreases, diffraction increases, as wavelength is kept constant..

Interference of Water Interference of Water WavesWaves

InterferenceInterference occurs when 2 waves in the occurs when 2 waves in the same medium interact.same medium interact.

The Superposition The Superposition PrinciplePrinciple• The The resultant displacementresultant displacement of two of two

simul-taneous waves (simul-taneous waves (blueblue and and greengreen) is the algebraic sum of the ) is the algebraic sum of the two displacements.two displacements.

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

screen. screen.

• The The resultantresultant wave is shown in wave is shown in yellowyellow..

Constructive Constructive InterferenceInterference

Destructive Destructive InterferenceInterference

Constructive Interference- two interfering waves have displacement in the same direction. The waves must be in phase and combine together.

Destructive Interference- two interfering waves have displacement in opposite directions when they superimpose. The amplitude of the superimposed wave is smaller then the interacting waves.

Constructive Constructive InterferenceInterference

Destructive Destructive InterferenceInterference

3 conditions for 3 conditions for Interference to occur:Interference to occur:

1.1. Short distance apart, so they can Short distance apart, so they can interact in same medium.interact in same medium.

2.2. Waves come together at a common Waves come together at a common point.point.

3.3. Waves must have same frequencies Waves must have same frequencies and fixed positions.and fixed positions.

• Continuous interference from two Continuous interference from two sources.sources.

• If the source of waves produces circular waves, then the waves will meet within the medium to produce a pattern.

• The pattern is characterized by a collection of nodes and antinodes referred to as antinodal lines and nodal lines.

• Figure 8 on p. 463

2 Point Source Interference2 Point Source Interference

Two Point Interference Two Point Interference PatternPattern

• When we have two identical point sources When we have two identical point sources that are side by side, in phase, and have that are side by side, in phase, and have identical frequencies, we can analyse the identical frequencies, we can analyse the interference pattern that is produced to interference pattern that is produced to learn more about the waves.learn more about the waves.

• ripple tank simulation of two point source ripple tank simulation of two point source pattern: pattern: http://www.falstad.com/ripple/

Two Point Interference Pattern

Sources

NodesAntinodes

Two Point Interference Pattern In the diagram, crests

are represented by thick lines and troughs are represented by thin lines. We get constructive interference then whenever a thick line meets thick line, or when a thin line meets a thin line. This constructive interference causes antinodes, shown by the red dots.

Thick line = crest

Thin line = trough

Two Point Interference Pattern Destructive

interference occurs whenever a thick line meets a thin line. These points form nodes, which are represented by a blue dot. The nodes and antinodes appear to ‘stand still’ which makes this a standing wave pattern.

Two Point Interference Pattern The number of nodal

lines increases when you do any of the following: Increase frequency of the

sources Decrease the wavelength

of the waves Increase separation

between the sources

https://www.youtube.com/watch?v=1FwM1oF5e6o

- -

• In 1801 In 1801 Thomas Young was able was able to offer some very strong to offer some very strong evidence to evidence to support the wave support the wave model of lightmodel of light..

• He placed a screen that had two He placed a screen that had two slits cut into it in front of a slits cut into it in front of a monochromatic light. light.

• The results of Young's Double The results of Young's Double Slit Experiment should be very Slit Experiment should be very differentdifferent if light is a wave or a if light is a wave or a particle.particle.

Young’s ExperimentYoung’s Experiment

Light as a ParticleLight as a Particle

Light as a Light as a WaveWave

In In Young’s experimentYoung’s experiment, light from a , light from a monochromatic source falls on two slits, monochromatic source falls on two slits, setting up an setting up an interference patterninterference pattern similar to that with water waves.similar to that with water waves.

Light source S

1

S2

Young’s Interference Young’s Interference PatternPattern

s1

s2

s1

s2

s1

s2

Constructive

Constructive

Bright fringe

Bright fringe

Dark fringeDestructive

- Interference of the waves determines the intensity of the light.

- The alternating areas of dark and light fringes are created by alternating areas of constructive and destructive interference.

Conditions for Bright Conditions for Bright FringesFringes

Bright fringesBright fringes occur when the difference in occur when the difference in pathpath is an integral multiple of is an integral multiple of oneone wave wave length length ..

pp11

pp22

pp33

pp44

What does this mean?What does this mean?

• Waves must be in phaseWaves must be in phase

• Path length needs to be a whole Path length needs to be a whole number wavelength difference number wavelength difference for for constructive interference constructive interference to to occur.occur.

• FORMULA for FORMULA for bright fringesbright fringes, , also known as also known as MAXIMAMAXIMA (ON (ON BOARD)BOARD)

Conditions for Dark Conditions for Dark FringesFringes

Dark fringesDark fringes occur when the difference in occur when the difference in pathpath is an odd multiple of one-half of a wave is an odd multiple of one-half of a wave length length ..

pp11

pp22 2

pp33

pp33

2p n

n n = = oddoddn n = =

1,3,5 …1,3,5 …

What does this mean?What does this mean?

• Waves must be out of phaseWaves must be out of phase

• Path length needs to be a half Path length needs to be a half number wavelength difference number wavelength difference for for destructive interference destructive interference to to occur.occur.

• FORMULA for FORMULA for dark fringesdark fringes, also , also known as known as MINIMAMINIMA (ON BOARD) (ON BOARD)

https://www.youtube.com/watch?v=Iuv6hY6zsd0

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

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

d sin

d

d sin nn = 1, 2, 3,

…

The Grating EquationThe 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

Example 2:Example 2: Light (Light (600 nm600 nm) strikes a grating ) strikes a grating ruled with ruled with 300 lines/mm300 lines/mm. What is the . What is the angular deviation of the angular deviation of the 22ndnd order order bright bright fringe?fringe?

300 lines/mm

n = 2

To find slit To find slit separation, we take separation, we take reciprocal of 300 reciprocal of 300 lines/mm:lines/mm:

10.00333 mm/line

300 lines/mmd

3mm 10 m0.00333

line 1 mmd

Lines/mm Lines/mm mm/linemm/line

-6 3 x 10 md -6 3 x 10 md

Example (Cont.) 2:Example (Cont.) 2: A grating is ruled with A grating is ruled with 300 lines/mm300 lines/mm. What is the angular . What is the angular deviation of the deviation of the 22ndnd order order bright fringe? bright fringe?

-9

-6

2 2(600 x 10 m)sin ;

3.33 x 10d

sin 0.360

2 = 21.102 = 21.10Angular deviation of Angular deviation of second order fringe second order fringe

is:is:

300 lines/mm

n = 2

sin 2d n n

-6 3 x 10 md = 600 nm

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

Interference From Single Interference From Single SlitSlit

Pattern Pattern ExaggeratedExaggerated

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

Relative intensity

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

When looking at single slit When looking at single slit diffraction we must assume:diffraction we must assume:

1.1.Slit width is narrow enough for Slit width is narrow enough for diffraction to occur. (NOT too small diffraction to occur. (NOT too small as thought it acts like a point as thought it acts like a point source)source)

2.2.Light is monochromatic with a Light is monochromatic with a λλ..

3.3.Light source is far enough from Light source is far enough from the slit to ensure all rays hitting the the slit to ensure all rays hitting the slit are parallel.slit are parallel.

The pattern observed from single slit diffraction is called Fraunhofer Fraunhofer diffraction. diffraction. (fig.2 p. 512)(fig.2 p. 512)

-This pattern shows a bright central fringe This pattern shows a bright central fringe called the central maximum and is called the central maximum and is flanked by less bright fringes called flanked by less bright fringes called secondary maxima and dark fringes secondary maxima and dark fringes called minima.called minima.

Huygen’s Principle helps to explain and predict the diffraction patterns. All points on a wave front can be thought of as new sources of spherical waves called wavelets. (diagram on board)

Single Slit Interference Single Slit Interference PatternPattern

a/2

aa/2

sin2

a

12

43

5

Each point inside Each point inside slit acts as a slit acts as a source. source. For rays 1 and 3 For rays 1 and 3 and for 2 and 4:and for 2 and 4:

sin2

ap

First dark First dark fringe:fringe:sin

2 2

a sin2 2

a

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

destructively.destructively.

Single Slit Interference Single Slit Interference PatternPattern

a/2

aa/2

sin2

a

12

43

5

sin2 2

a

First dark First dark fringe:fringe:

sina

sina

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

Example 3:Example 3: Monochromatic light shines Monochromatic light shines on a single slit of width on a single slit of width 0.45 mm0.45 mm. On a . On a screen screen 1.5 m1.5 m away, the first dark fringe is away, the first dark fringe is displaced displaced 2 mm2 mm from the central from the central maximum. What is the wavelength of the maximum. What is the wavelength of the light?light?

x = 1.5

m ya = 0.35 mm

= ?

sina

sina

ysin tan ; ;

x

y ya

x a x

(0.002 m)(0.00045 m)

1.50 m = 600

nm

Diffraction for a Circular Diffraction for a Circular OpeningOpening

Circular diffractionCircular diffraction

D

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

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

Resolution of ImagesResolution of 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.

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 LimitResolution Limit

d2

Resolution limit

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

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

Resolution Resolution LimitLimit

Separate Separate imagesimages

Resolving Power of Resolving Power of InstrumentsInstrumentsThe 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 and the limiting angle of resolution for a limiting angle of resolution for a

circular opening is:circular opening is:

For small angles, For small angles, sin sin ,,and the and the limiting angle of resolution for a limiting angle of resolution for a

circular opening is:circular opening is:

Limiting angleLimiting angle

D

Resolution and DistanceResolution and Distance

Limiting Angle of Resolution:

00 1.22

s

D p

ssoo

pp

D

Limiting angle Limiting angle oo

Example 4:Example 4: The tail lights (The tail lights ( = 632 nm = 632 nm) ) of an auto are of an auto are 1.2 m1.2 m apart and the pupil apart and the pupil of the eye is around of the eye is around 2 mm2 mm in diameter. in diameter. How far away can the tail lights be How far away can the tail lights be resolved as separate images?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

SummarySummary

Bright fringes:

, 0, 1, 2, ...dy

n nx

Dark fringes:

, 1, 3, 5...2

dyn n

x

Young’s Young’s Experiment:Experiment:

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

x

y

d sin s1

s2

d p1

p2

sindy

dx

Summary (Cont.)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.)Summary (Cont.)

Pattern Pattern ExaggeratedExaggerated

Relative Intensity

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

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

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

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

Summary (cont.)Summary (cont.)

Limiting Angle of Resolution:

00 1.22

s

D p

ssoo

pp

D

Limiting angle Limiting angle oo

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

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

CONCLUSION: Chapter 37CONCLUSION: Chapter 37Interference and Interference and

DiffractionDiffraction