**Young's Double Slits**

**Waves 10**

Variation of intensity of light can be explained if light behaves like a wave.

Light waves coming from each slit are interfering with each other.

Superposition at the screen leads to regions of constructive interference (bright fringes) and regions of destructive interference (dark fringes).

Putting it all together...

Problem

How can we relate the observed interference pattern to our model in order to make a prediction?

We know adjacent fringes will be separated by an angle, but we can only measure the distance between , y.

By drawing a diagram is it possible to relate y to the angle of separation?

Coherence

When waves have a constant phase relationship.

Only true for waves of the same wavelength, frequency and wavespeed.

**Objectives**

**Results**

Realisation

What was Young's evidence for light being a wave?

Can predict the interference pattern produced?

How do we relate observations

to theory?

Ray Diagram

Young's double slits is an example of two source interference.

Observations explained through superposition of two waves.

Waves must be coherent for interference pattern to be observed.

What is coherence?

How does this affect intereference?

Constructive interference Destructive Interference

Conditions for interference

Path difference between waves is a whole number of wavelengths

Path difference between waves is an odd number of half wavelengths

Constructive: l = n Destructive: l = (n +1/2)

Where l is the path difference, is the wavelength and n is an integer

Superposition must occur in order to for an interference pattern

What is superposition?

Questions to consider

Where is the source of my waves?

Where is superposition taking place?

Why do my waves travel different paths?

Important Math

Wave Equation

Trigonometry

Conditions for interference

Will help to understand coherence

Will allow us to define a path length difference

Will let us relate geometry of experiment to observations

Diffraction

Waves spread out when passing through a gap of similar width to there wavelength

Construct a ray diagram showing the two possible paths light can travel from the source to a point on the screen

How can we use this to find the path length difference?

Set-up

Point on screen

Point on screen

Slit 1

Slit 2

Source

Path length difference

Applying a little math

Something about this diagram seems wrong...

surely the light is leaving the slits at different angles...

Let's say that

L>>d

so the difference in angle is really small...

the lines appear almost parallel now

the angle is very small

path length difference very small

L

d

Light has a very small wavelength (300-600nm) so we would expect path length difference to be very small.

Observations

For single slit light diffracts as expected

For double slit there is a regular variation in intensity

There is a bright central fringe of light.

Bright fringes are formed at regular spacings.

Intensity decreases as you move away from centre

Max and min intensities result of superposition

An interference pattern is being observed

path length difference = l = dsin(-)

where d is the distance between slits and (-) is the angle formed by the ray and a line perpendicular to the screen.

for constructive interference l = n

therefore sin(-) = n /d

where is the wavelength of light

for destructive interference l = (n+1/2)

therefore sin(-) = (n+1/2) /d

where is the wavelength of light

Ray diagram

double slits

(-)

Central Bright Fringe

Position of first bright fringe

y

L

From trigonometry

Tan(-) = y / L

Making a prediction

We expect the angle at which bright fringes to form to be...

sin(-) = n /d

...and we can relate the angle to our measured separation as...

Tan(-) = y / L

...as the angle is really small we can say...

Tan(-) = sin(-)

y / L = n / d

So now we can plot a graph of y against n...

y = n L / d

If we get a straight line with a gradient equal to

L

/

d

we will have strong evidence our theory is correct!

Results Table

Graph

Conclusion

Was gradient of graph in agreement with theory?

How accurate were your results in terms of percentage uncertainty?

How could we refine/extend this experiment for further study?