Interference

Superposition in waterCreate your own wave superposition in your tub.

Take a photograph and print off a picture

Show on the picture where the waves have a

supercrest, where they have a supertrough Where a crest meets a trough

and the resultant displacement is zero

Hearing superposition

1m

Same frequency fromSignal generator

Walk along a path that is one metre away

What do you hear?

Today you will...

Find out about interference patterns and answer these questions

What are coherent sources? What is the general condition for the formation of a bright fringe?Are Young’s fringes equally spaced?What factors could be (i) increased or (ii) decreased, to increase the fringe spacingWhy are slits used, rather than two separate light sources, in Young’s double slits

experiment?What are the roles of diffraction, and interference, when producing Young’s fringes?What do we mean by diffraction? What feature of two waves must combine in order to produce reinforcement?What is the phase difference between two waves if they produce maximum

cancellation?Why is total cancellation rarely achieved in practice?

Thomas YoungNewton’s view that light was

made from particles was questioned by young in his

‘Young’s double slit’ experiment.

The experiment showed that light had wave properties

because they formed interference patterns.

Interference patterns happen for light, water and sound.

http://www.youtube.com/watch?v=DfPeprQ7oGc

The Interference Pattern

The laser interferenceLaser light is highly monochromatic (only gives out 1 frequency of light)

The emitted light is also coherent(of the same phase)

This gives a very sharp image

What are the factors that affect fringe separation?

Fringe separation = distance between bright lines

Fringe separation

w = separation of the fringes (bright to bright or dark to dark)

λ = wavelength of the lights = separation of the two slits

D = distance between slits and screen

w

D

s

W = λDS

Young’s QuestionsFinding the wavelength of sodium lightIn a two-slit apparatus the slits are 0.3 mm apart. Fringes in sodium are observed at a

distance of 1.2 m from the slits. The separation of the fringes is 2.4 mm.1. What is the wavelength of sodium light? 2. The same light gives a fringe separation of 3.6 mm with a different pair of slits. What

is the slit separation if the distance between the slits and the fringes is the same? Red light of wavelength 7.0 x 10–7 m is shone at right angles through two slits of

separation 0.3 mm. Fringes are formed at a distance of 1.3 m from the slits.3. What is the fringe spacing? 4. The same light gives a fringe spacing of 2 mm when passed through a different pair

of slits. What is the slit separation if the distance between the slits and the fringes is the same?

In a two-slit apparatus the slits are 0.3 mm apart. White light passes through the slits and fringes are observed at a distance of 2 m from the slits. Red light has a wavelength of 700 nm and blue light has a wavelength of 400 nm.

5. Calculate the fringe spacing for each colour. 6. Use your answers to explain the coloured fringes seen on the screen.

W = λDS

Young’s answers

Ripple Tank

The geometric analysis of Young’s experiment

Young’s two-slit interference experiment

narrowsource

two slits: 1 mmspacing or less

bright anddark fringes

several metres several metres

screen

Bright fringe at centre

to central brightfringe on screen

d

waves in phase:path difference = 0

s

What is the use of knowing θ?

fromsource d

light combinesat distant screen

slit-screen distance L

fringespacing x

Geometry of two-slit experiment

x/L = sin approximately

For it to be in phase (first fringe)θ = sin-1 d/λ

For it to be out of phase θ = sin-1 2d/λ

At the first dark fringe

d sin = /2

d

waves in anti-phase:path difference = /2path difference = d sin

to dark fringe on screen

Light going to first dark fringe

The waves must be in anti-phaseλ\2 difference at the point on the wall

λ\2 = s sin θθ = sin-1 2d/λ

θ

s

θ

What is this length?O = s sin θ

OppositeSin θ Hypotenuse

s

s

At the first Bright fringeFirst bright fringe off centre

to brightfringe onscreen

d sin =

d

waves in phase:path difference = path difference = d sin

The waves must be in phaseλ difference at the point on the wall

λ = s sin θθ = sin-1 s/λ

s

s

s

What is the use of knowing θ?

fromsource d

light combinesat distant screen

slit-screen distance L

fringespacing x

Geometry of two-slit experiment

x/L = sin approximately

For it to be in phase (first fringe)θ = sin-1 d/λ

For it to be out of phase θ = sin-1 2d/λ