3.2.1

# Interference

Test yourself

## Path Difference and Coherence

To understand interference and diffraction patterns, it is important to understand path difference and coherence.

### Coherence

• Interference happens when any two waves are superimposed on one another.
• But in most cases, this creates a very messy wave pattern.
• To see a clear interference pattern, we need two waves that are coherent.
• Coherent means that the two waves must have the same frequency and wavelength, and have a fixed phase relation.
• Usually this fixed phase relation is zero.

### Path difference

• The path difference between two waves is the difference in length travelled by the waves to get to a certain point.

### Path difference and interference

• For two coherent wave sources:
• If the path difference is a multiple of λ, the waves will be in phase and we will see constructive interference:
• Path difference $= nλ$
• If the path difference is a whole number plus a half λ, the waves will be exactly out of phase and we will see destructive interference:
• Path difference $= (n+\frac{1}2)\lambda$

## Young's Double-Slit Experiment

Young's famous double-slit experiment deals with the interference from two monochromatic, coherent sources. Monochromatic means all light is of the same wavelength.

### Producing coherent waves

• To observe interference between two waves, we need two coherent sources.
• We can use two separate sources for this - but it is often tricky to make sure they are coherent.
• A useful trick is to shine a laser through two slits.
• The laser produces monochromatic, coherent light.
• The two slits then act like two identical sources of laser light.
• The slits must have the same size and be comparable to the wavelength of the laser light to diffract it.

### Experiment layout

• The diagram shows the production and interference of two coherent, monochromatic light waves.
• This produces a series of light and dark fringes corresponding to constructive and destructive interference.

## Fringes in Young's Double Slit Experiment

We can calculate the spacing of fringes seen in the double-slit experiment.

### Fringe spacing

• To calculate the spacing between bright fringes in the double-slit experiment, use the following equation:
• $w = \frac{\lambda D}{s}$
• Where the fringe spacing is w, the wavelength is λ, the spacing between slits is s, and the distance from the slits to the screen is D.

### Average over many fringes

• Normally, the fringe spacing is very small.
• To ensure our measurement is accurate we measure across lots of fringes and divide by the number of fringe widths to find an average.

### Using white light

• We can use white light instead of laser light in a double slit experiment.
• Instead of clear bright and dark fringes:
• The middle fringe is just bright white light.
• All fringes are more spread out.
• Side fringes have a spectrum of visible colours. Blue light diffracts less than red so is nearer the centre of the screen.