Interference of waves

Wavefronts and direction of propagation

• The crests/troughs of a wave are sometimes called wavefronts.

• The shape of a wave is determined by its wavefronts.

• The direction of propagation of the wave is perpendicular to wavefronts

Wavefront

Direction of wave

PhaseParticles moving in the same motion all the time are in phase. Particles moving oppositely all the time are in opposite phase. If particles are not always moving in the same direction, they are out of phase.

F

A

B

C

D

E G

H

wave propagation

Phase differencePhase difference is expressed in wavelength.The distance between two points in phase is

a whole number of wavelength (nλ).The distance between two points in

opposite phase is an odd number of half wavelength ((2n+1) λ /2).

Two waves are in phase

Two waves are in opposite phase

Two waves are out of phase

InterferenceWhen two waves meet in the same medium, the vibration intensifies at some places and weakens at others. This phenomenon is called interference. If the vibration is larger than individual waves, the interference is called constructive interference (superposition). If the vibration is smaller than individual waves, it is destructive interference (superposition).

Wave interference

constructive interference destructive interference

Simply align the waves in time and add the displacements.If the displacements are of the same sign, the wave is reinforced and grows bigger – constructive interference.If the displacements are of opposite sign, the wave is diminished and becomes smaller – destructive interference.

Interference patternsantinodal lines

nodal lines

Any point on the antinodal lines the path difference is a whole number of the wavelength, eg: S1P-S2P=7.5 λ – 6.5 λ =λAny point on the nodal lines the path difference is an odd number of the half wavelength, eg: S1Q-S2Q=6 λ – 7.5 λ =1.5λ

S1 S2

PQ

Young’s double slit experiment device

When light passes through a slit it is diffracted, acting as a light source. When the light passes through a pair of slits (carefully placed the right distance from the original slit), it is diffracted. The slits behaved as if they were also individual sources of light. The light interferes and forms patterns on the screen.

Young’s double slit experiment

Young’s double slit experiment

The interference patterns consist of a series of evenly spaced dark and bright lines called fringes. The bright fringes are caused by constructive interference , while the dark fringes are the result of destructive interference.

First conducted in 1801, this experiment established the wave nature of light. Young's double slit experiment is a typical experiment to show the diffraction and interference of light.

Double slit experiment

θ

x

L

S1

S2

d

P

Screen

The path difference from two sources at point P is:pd =S2P-S1P= dsinθWhen dsinθ = nλ, P is on a bright fringe.When θ is small, sin θ =tan θ =x/L, For monochromatic light, dx/L = nλ gives the position of bright fringe.The spacing of fringes is given by x = λL/d

ExampleDescribe and explain how the spacing of an interference

pattern is affected bya. The wavelength of a wave.b. The distance from the screen.c. The separation of the sources.Ans: the spacing is determined by x = λL/d.The spacing is proportional to wavelength λ. When λ

increases, the spacing increases; The spacing is proportional to the distance. When L increases,

the spacing increases; The spacing is inversely proportional to the separation, when

d increases, x decreases.

Multiple source interferenceDiffraction grating: a series of many fine parallel slits,

evenly spaced on a piece of glass or plastic. Slit spacing d is given by the number (N) per metre: d = 1/N.

Interference patterns similar to double slit pattern. Main differences:

1. The slits are very thin so light is diffracted through a wide angle.

2. Slits are so closely spaced so the bright fringes are widely spread.

3. There are large number of slits, so fringes are bright.

θ

x

L

d

P

Screen

generally: dsinθ =nλ (n =0, 1, 2, …)

Interference pattern formula

nL

dx

L

x ,sinWhen L >>x,

eg: Light from a red laser (wavelength 6.70x10-7m) is

shone on a diffraction grating. The light forms a pattern showing nine bright fringes spread across a distance of 4.0cm. When the laser is replaced with a green laser, the interference pattern shows nine fringes spread out over a distance of 3.2cm. Calculate the wavelength of the green laser.

Ans:

spacing:

so ie:

d

Lx

constx

d

L

g

g

r

rxx

mx

x

x

x

r

rg

r

rgg

77

1036.504.0

1070.6032.0

8

8

Interference of white lightAntinodal lines for different wavelengths

(frequencies) of same order spread out except the zero order. The red light bends more than violet light. The diffraction grating produces a series of spectra on both sides of a central white line.

Interference of waves

Rippletank Demo