For an interference pattern to be observable,

1. The waves must be of the same type and must meet at a point.
2. The waves are coherent, i.e. the waves from each source maintain a constant phase difference.
3. The waves must have the same wavelength and roughly the same amplitude.
4. The waves must be both either unpolarised or have the same plane of polarisation.

Two sources are said to be coherent if waves from the sources have a constant phase difference between them.

Young’s Double Slit Experiment A simple experiment of the interference of light was demonstrated by Thomas Young in 1801. It provides solid evidence that light is a wave.

Interference fringes consisting of alternately bright and dark fringes (or bands) which are equally spaced are observed. These fringes are actually images of the slit.

At O, a point directly opposite the mid-point between S1 and S2, the path difference between waves S2O – S1O is zero. Thus constructive interference occurs and the central fringe or maxima is bright.

Suppose P is the position of the nth order bright fringe (or maxima). The path difference between the two sources S1 and S2 must differ by a whole number of wavelengths.

S2 P –S1 P = nλ

As the distance D is very much larger than a, the path difference S2 P – S1 P can be approximated by dropping a perpendicular line S1 N from S1 to S2 P such that S1 P ≈ NP and

the path difference S2 P –S1 P ≈ S2N = nλ

From geometry, S2N = a sin θ where a is the distance between the centres of the two slits.

Equating, a sin θ = nλ and re-arranging, sin θ = nλ/a

But from geometry, tan θ = xn / D where xn = distance of nth order fringe from the central axis Since θ is usually very small, tan θ ≈ sin θ i.e. xn / D = nλ/a or xn= nλD/a

Thus the separation between adjacent fringes (i.e. fringe separation) is,

Δx = xn+1 – xn = (n+1) λ D/a – nλ D/a = λD/a

Thus,

Fringe separation Δx = λ D/a

Clearly Δx is a constant if λ, D and a are kept constant. If all factors are kept constant, the fringes are evenly spaced near the central axis.