WAVE INTERFERENCE....

INTERFERENCE

Interference patterns are a direct result of superpositioning. Antinodal and nodal lines are produced. These patterns can be enhanced using diffraction gratings, where all waves pass through each other from multiple point sources.We also learnt that the path difference for a point on a an antinodal line is always a factor of a wavelength, , whereas for a nodal line is half a wavelength, ½.Antinodal line path difference = nNodal line path difference = n½

Where n = order 0, 1, 2, 3, …….

Birds eye view of 2 waves....

Red: crest meets crestOr trough meets trough.Constructive interference

Blue: crest meets a trough and they cancelout. Destructive interference

Order of magnitude (m)

Can be used to calculate the path difference.

Whole numbers: antinodal linesHalf numbers: nodal lines

Path Difference

6 wavelengths5

wavelengths

S1

S2

S1 and S2 are two coherent sources

All points on a wavefront are in phase with one another

Waves interfere constructively where wavefronts meet. = antinodal lines

Along the nodal lines, destructive interference

occurs.Here antiphase

wavefronts meet. Wave Intensity(Fringes)

0

1

12

2

n = order number

Doubleslit

Screen

Monochromatic light, wavelength

Young’s Double Slits A series of dark and bright

fringes on the screen.

Young’s Double Slit Experiment THIS RELIES INITIALLY ON LIGHT

DIFFRACTING THROUGH EACH SLIT.

Where the diffracted light overlaps,

interference occurs

Doubleslit screen

Light

INTERFERENCE

Diffraction

Some fringes may be missing where there is a

minimum in the diffraction pattern

A

BP

Wave trains AP & BP have travelled the same distance(same number of

’s)

Assuming the sources are coherent

Hence waves arrive in-phase

CONSTRUCTIVE INTERFERENCE(Bright fringe)

L

Screen

Slits

d

d = slit separation

x = fringe separation

Ldxn

Normal light sources emit photons at random, so they are

not coherent.

LASER

LASERLASERS EMIT COHERENT LIGHT

Example 5:Monochromatic light from a point source illuminates two parallel, narrow slits. The centres of the slit openings are 0.80mm apart. An interference pattern forms on screen placed 2.0m away. The distance between two adjacent dark fringes is 1.2mm.Calculate the wavelength, , of the light used.

Example 5:Monochromatic light from a point source illuminates two parallel, narrow slits. The centres of the slit openings are 0.80mm apart. An interference pattern forms on screen placed 2.0m away. The distance between two adjacent dark fringes is 1.2mm.Calculate the wavelength, , of the light used.

SOLUTION:The distance to the screen (2.0m) is large compared with the fringe spacing (1.2mm). The approximation formula can be used.n = dx/L [n = 1 because the fringe spacing is being calculated] = (8.0 x 10-4 x 1.2 x 10-3) / 2.0 = 4.8 x 10-7 m

WAVE INTERFERENCE....

Decide which points are Constructive interference and which are Destructive interference?

Interference

In phase

Out of phaseBy 180 deg (half a wavelength)

Youngs Double Slit Experiment

Quantum Physics.http://www.doubleslitexperiment.co

m/

Changing slit separation

Double slit animation.http://www.colorado.edu/physics/200

0/schroedinger/two-slit2.html

A student uses a laser and a double-slit apparatus to project a two-point source light interference pattern onto a whiteboard located 5.87 meters away. The distance measured between the central bright band and the fourth bright band is 8.21 cm. The slits are separated by a distance of 0.150 mm. What would be the measured wavelength of light?

Ldxn

Changing slit separation.

Changing wavelength

Path Difference

PD= m λ

Two point sources, 3.0 cm apart, are generating periodic waves in phase. A point on the third antinodal line of the wave pattern is 10 cm from one source and 8.0 cm from the other source. Determine the wavelength of the waves.

Two point sources are generating periodic waves in phase. The wavelength of the waves is 3.0 cm. A point on a nodal line is 25 cm from one source and 20.5 cm from the other source. Determine the nodal line number.

The Diffraction Grating: This is a piece of glass with tiny slits made in it to produce small point sources. A formula can be used to relate to the interference pattern produced by a particular diffraction grating.

dsin = n

(Where n = 0, 1, 2, 3 …….)Often N, the number of slits per metre, or slits per centimetre is given. The slit spacing d is related to N by:

d = 1/N

Grating

Monochromatic light C

For light diffracted from adjacent slits to add constructively, the path difference = AC must be a whole number of wavelengths.

AC = AB sin and AB is the grating element = d

Hence d sin n

d = grating element

metreperlinesofnumberd 1

A

B

DIFFRACTION GRATING WITH WHITE LIGHT

Hence in any order red light will be more diffracted than blue.A spectrum will result

nmnm lightvioletlightred 400,700

White Central maximum, n = 0

First Order maximum, n = 1

First Order maximum, n = 1

Second Order maximum, n = 2

Second Order maximum, n = 2

Several spectra will be seen, the number

depending upon the value of d

nd sin

Grating

screen

n=0n=2 n=1n=3

grating

Note that higher orders, as with 2 and 3 here, can

overlapNote that in the

spectrum produced by a prism, it is the

blue light which is most deviated

Example: Light from a laser passes through a diffraction grating of 2000 lines per cm. The diagram below shows the measurement made.

laser 0 order

2nd order

0.5mGrating

2m

Calculate the wavelength of the light.

SOLUTION:

Slit spacing d = 1/N= 1/200000

= 5.00 x 10-6m

sin = 0.5/2

= 0.250

= dsin/n

= (5.00 x 10-6 x 0.250) / 2

= 6.25 x 10-7m

http://webphysics.ph.msstate.edu/javamirror/ipmj/java/slitdiffr/index.html