4.4d Interference

THE IB SAYS

Essential idea: Waves interact with media and each other in a number of ways that can be unexpected and useful.

Understandings: Interference patterns; Double-slit interference; Path difference

Applications and skills: Quantitatively describing double-slit interference intensity patterns

Guidance: Students will not be expected to derive the double-slit equation; Students should have the opportunity to observe diffraction and interference patterns arising from more than one type of wave

Data booklet:

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Interference

Two or more wave sources whose waves are passing through the same medium at the same time will interfere in accordance with the principle of superposition.

If these waves are identical apart from their initial position (identical in terms of wavelength, frequency, phase, etc) then a clearly defined wave pattern, showing zones of constructive and destructive interference, will be formed, as can be seen in the screenshot above for water waves. The same principles can be applied to all 2D and 3D waves, including water, sound and light.

Path difference

Constructive interference will occur when the maximum displacement for both wave sources occurs at the same point in space - in other words they are at the same phase at that point in space. Destructive interference will occur when the 'crest' from one wave coincides with the trough from another - in other words they are completely out of phase at that point.

Another way to consider the situation is to look at the path difference. The path length is the distance between a wave source and a point along that wave. The difference between two path lengths is the path difference. If the path difference from a single point in space to two different wave sources is either zero or an integer number of wavelengths (path difference = nλ) then there will be constructive interference. If the path difference is zero or an integer plus half a wavelength (path difference = (n + 0.5)λ ) then there will be destructive interference.

Relating slit separation, screen distance, distance to first maxima and wavelength

These four values are all related using the equation given in the data booklet. For SL you don't need to know the derivation of this equation, although for HL it is very useful. When deriving or applying this equation you must remember it is only valid for situations when the distance from slits / sources to the screen or equivalent is significantly greater than the separation of the slits.

Additional videos

A great introduction and recreation of the original double-slit experiment.

The first of a brief playlist looking at the Double Slit, mathematics and worked examples

This video from MIT has no commentary but very nicely demonstrates (from 1:43) double slit interference through identical slits but with lasers of different wavelengths.

The Double-Slit Experiment and Quantum Mechanics

This video starts with a (good) generic explanation of double-slit interference, before introducing one of its stranger applications.

Resources from textbooks

Oxford Physics: pages 152 - 157, good detailed and with worked examples

Hamper HL (2014): page 176 introduces interference in the context of water waves, pages 193 - 194 consider two-slit interference of light

Hamper SL (2014): page 165 looks at interference in water and page 175 looks at two-slit interference of light.

Relevant questions from Dot Point Physics (4 Oscillations and Waves)

pages 216 - 221

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