What you are looking at
A wave of light arrives from the left and passes through a
single narrow slit. Instead of
casting a sharp shadow of the opening, the light
spreads out — this is
diffraction. On the screen you see a wide, bright
central band with a
series of much dimmer fringes on either side, separated by dark minima. The glowing field shows the
time-averaged wave intensity; the strip on the right is the screen pattern, plotted as the curve.
Why a single slit makes fringes
By Huygens' principle every point across the slit opening acts as its own little wave source. To reach a
point on the screen, the wavelets from different parts of the slit travel slightly different distances and
so arrive out of step. Straight ahead they all agree and add up — the bright centre. At certain angles the
wavelets pair up and cancel exactly, giving a
dark minimum. The first minimum occurs when
the path difference across the whole slit is one wavelength:
a sin θ = m λ (m = ±1, ±2, … — these are the dark fringes)
Note this is the condition for
minima, not maxima. The bright
central maximum is
twice as wide as the side fringes, and its angular half-width is
sin θ ≈ λ / a → width ≈ 2 λ L / a
The width is inverse to the slit
The key, and counter-intuitive, result: a
narrower slit produces a
wider
pattern. Squeeze the opening down (small a) and the light fans out dramatically; open it up (large a) and
the central band shrinks toward a sharp bright line — the ray-optics shadow you would expect. A longer
wavelength also spreads more, so red diffracts more than violet.
Things to try
Shrink the
slit width and watch the central band balloon outward, with the side fringes
following. Sweep the
wavelength from violet to red to see the whole pattern stretch.
Diffraction like this sets the ultimate resolution limit of cameras, telescopes and microscopes — two
objects can only be told apart if their diffraction blobs do not overlap too much.