Single-slit diffraction

When light passes through a narrow slit, it spreads into the region beyond the slit. This spreading is called diffraction. Light from different parts of the slit overlaps: in some directions it reinforces, producing bright regions, while in others it cancels, producing dark regions.

Monochromatic light through a single slit

With monochromatic light—light of a single wavelength—the pattern has a bright central maximum directly opposite the slit. It is bounded on both sides by dark minima. Beyond these are weaker secondary maxima, separated by further dark minima.

The central maximum is broader than the secondary maxima. Its angular width is the angle between the directions of the first dark minima on either side of the centre.

The central maximum becomes wider as the wavelength increases, and narrower as the slit width increases. Diffraction is therefore more pronounced when the slit is narrow relative to the wavelength.

White light through a single slit

White light contains a range of wavelengths. At the centre of the pattern, these wavelengths overlap, so the centre appears white. Away from the centre, each wavelength spreads by a different amount: shorter wavelengths appear closer to the centre, while longer wavelengths extend farther out. This produces coloured fringes, which can overlap.

Transmission diffraction gratings

A plane transmission diffraction grating has many parallel slits separated by equal distances. Light passing through each slit diffracts, and the diffracted waves overlap and interfere. In certain directions, the waves reinforce one another to produce bright principal maxima.

When light is incident normally on the grating, it travels perpendicular to the plane of the grating, so the waves at adjacent slits start in phase. In a direction at angle $$\theta$$ to the normal, a wave from one slit travels farther than a wave from the adjacent slit. The difference in their distances is:

Here, $$d$$ is the slit spacing. The angle $$\theta$$ is measured from the normal to the grating.

Principal maxima and diffraction order

A principal maximum occurs when the path difference between waves from adjacent slits is a whole number of wavelengths. The waves then arrive in phase and interfere constructively. For wavelength $$\lambda$$, the condition is:

The integer $$n=0,1,2,\ldots$$ is the order of the maximum. The zero-order maximum lies along the normal: the light is undeviated. First-order, second-order and higher-order maxima occur on either side of the normal. An order can occur only if $$n\lambda\leq d$$, since $$\sin\theta$$ cannot be greater than one.

Separation of wavelengths

For a given non-zero order and slit spacing, a longer wavelength requires a larger value of $$\sin\theta$$ and therefore appears at a larger angle from the normal. A grating consequently separates light containing multiple wavelengths into spectra. The wavelengths overlap at the undeviated zero-order maximum.

The grating equation can be used to measure a wavelength from its diffraction angle, order and slit spacing. Spectral features can also be analysed to identify substances from their emission or absorption spectra.