Interference & Diffraction

Terminology

Interference takes place when waves interact - e.g. waves from two or more loudspeakers. Interference can be constructive or destructive, and the effects are due to the superposition of the waves.

Diffraction occurs when a wave encounters an obstacle it can't pass through. There is a bending of waves around small obstacles and the spreading out of waves passing through small gaps between two obstacles. It is most pronounced when the wavelength is roughly similar to the dimensions of the diffracting objects or the opening through which it is passing. Because of this diverging effect, interference between different parts of this wave occurs, producing interference patterns.

(Diffraction is not to be confused with refraction, in which there is a change of direction of a wave resulting from a change in refractive index of the medium through which the wave is travelling.)

Interference occurs with all waves, including sound waves, water waves, and electromagnetic waves such as visible light, x-rays and radio waves. As physical objects have wave-like properties (noticable at and below the atomic level), diffraction also occurs with matter and can be studied according to the principles of quantum mechanics.

When we are referring to a wave emerging from a single slit or an obstacle, we tend to use the term "diffraction" as there is no other wave apart from itself to interfere with. With a few slits - especially the double-slit situation - we tend to describe the overall phenomenon as "interference", although each wave emerging from a slit is diffracting. Perversely, once we get to many slits, we tend to describe the overall phenomenon as "diffraction" as we did for one slit- consider for example the "diffraction" grating. This use of terms is not logical (as with some other areas of physics); it's just the convention!

Band = fringe (they can be bright or dark)

Maximum = brightest part of a bright fringe
Minimum = darkest part of a dark fringe

 

INTERFERENCE FORMULAE
λ = wavelength; θ = angle diffracted beam makes with axis; d,s = slit separation;
a = width of each slit (often denoted by 'b'); D = distance between slits and screen; w = width of a fringe

 

Multiple Sources/Slits

Single Slit

More accurate formulae

nλ = d sin θn(max)

where n=0,1,2,3,4,5,...
and θn(max) is the diffraction angle of the nth maximum.

'A' level syllabuses use this version for
diffraction gratings.

Similar formula to the multiple slit one, except use 'a' and 'θn(min)' instead of 'd' and 'θn(max)'

For the first minimum, this becomes:

sin θ = λ/a

The AQA B syllabus uses this version for the single "slit", referring to sin θ as the half-beam width in the context of satellites & loudspeakers.

Since λ << a, sin θ ≈ θ, so θ ≈ λ/a

Approximation for large D, i.e.
D >> d,s
D >> a

w ≈ λD/s

since sin θ ≈ w/D.
's' traditionally gets used here rather than 'd'.

'A' level syllabuses use this version for
Young's double slits.

w ≈ λD/a

The central fringe width is 2w

The AQA A and most syllabuses use this version for the single slit.

 

 

 

Single slit diffraction graph

Derivation of Single slit diffraction formula [from http://hyperphysics.phy-astr.gsu.edu]

INTERFERENCE JPATTERN FROM SATELLITE DISH

Diffraction Envelope