Interference of Waves

When two waves meet, they overlap/combine - This is known as interference. Interference of of this type can only happen between waves, implying that if light can show interference, then this "proves" light is a wave.

There are two types of interference:

Constructive Interference - When 2 wave crests or 2 wave troughs arrive at the same point at the same time, they are said to be in phase. The superposition of these two waves results in a stronger signal.

Destructive Interference - When a wave crest and a wave trough arrive at the same point at the same time, they are said to be out of phase. The superposition of these two waves causes the signals to be cancel each other out.

Coherence

In order to show light acting as a wave, we must first ensure that the waves we are trying to observe are coherent.

A coherent source has :-

1. Same Frequency

2. Same Wavelength

3. Same wave speed

4. Constant Phase relationship


In order to make light obey these rules, we must somehow convert one light source into acting as two.


Young's Double Slit Experiment

In 1801, Thomas Young performed a series of experiments, designed to prove that light was a wave. These experiments form the basis of our understanding of the wave nature of light, and interference patterns. In order to produce coherent waves Young scored two fine lines, slits, on a blackened plate of glass. Light from a single source could then split into 2 coherent ‘point’ sources by diffraction.

The video below gives a short introduction to the concept of Interference, as well as looking at the confusion this can occur!

Using a pair of compasses and two difference coloured pencils, recreate the diagram below of a double source Interference. (sources 3cm apart, wavelength 2cm)

In the above pattern, the following applies:-

1. Red dots - points of constructive interference (peak meets peak).

2. Blue dots - points of destructive interference (peak meets trough).

If a line is cut horizontally across the above diagram, you get the following series of constructive and destructive interference points.

Points of constructive interference gives strong/bright maxima.

Points of destructive interference give weak/dark minima.

In order to explain the shape of the two patterns above, we must look at each of the two colour points separately.


Path Difference and Interference

The pattern above always looks the same for a double slit, with a central bright maximum and a series of bright and dark bands, moving out symmetrically.

Central bright maximum - the waves from each source travel the same distance (path difference = 0) to reach this point. As the waves are coherent, this means that if they travel the same distance, then the waves will be in phase when they meet. This causes constructive interference and a central bright maximum.

Note - The central maximum is referred to as the 0th Order maximum.

To reach other maxima or minima, waves from the 2 sources have to travel different distances - the difference between these 2 distances is known as the path difference.

First (bright) maximum - As this is a bright band, the waves must meet in phase. This means the distance from the Slit S2 to the screen is greater that the distance from Slit S1 to the screen by 1 whole Wavelength. This applies for each maxima out from the centre, giving the general rule:-

Path difference = mλ

Where m = number of maxima out from centre.

First (dark) minimum - As this is a dark band, the waves must meet out of phase. This means that a peak meets a trough, which means the waves are a half Wavelength out of step. This applies to each minima out from the centre, giving the general rule:-

Path difference = (m + ½) λ

Where m = number of maxima out from centre.