Waves and Light: Diffraction Gratings

Overview of Diffraction Gratings

A diffraction grating is a device that splits light into its component wavelengths, producing a spectrum.
It consists of a large number of equally spaced parallel slits (or lines), which cause incident light to be diffracted into multiple directions. The number of slits per metre is known as the grating spacing (d).
Each light wave passing through the slits interferes with the others to produce a pattern of constructive and destructive interference.
The bright spots, or maxima, are produced by constructive interference where the path difference between the waves is exactly a whole number of wavelengths, while dark spots or minima signify destructive interference.

The formula nλ = d sin θ describes the relationship in a diffraction grating, where: - n is the order of the maximum, - λ is the wavelength of the light, - d is the grating spacing, and - θ is the angle to the bright fringe from the perpendicular central maximum.
This formula shows that for each order (n), there is an angular position where constructive interference will occur for light with wavelength λ.

The order of maxima (n) refers to the number associated with each bright fringe. The central maximum is zero order, the next fringes each side are first order, and so on.
Different colours of light will diffract through different angles because they have different wavelengths.
For high orders, different colours may overlap. There is a limit to the number of orders, because sin θ will exceed 1 if the angle gets too large.

Spectroscopy, or the study of the interaction between matter and electromagnetic radiation, is heavily reliant on diffraction gratings to produce spectra.
CD and DVD players use diffraction gratings to read the data stored on the discs. The pit pattern on the disc acts like a grating, reflecting light in a way that can be interpreted as binary data.
In barcode scanners, a diffraction grating splits a laser beam into several beams, reading the barcode from multiple angles.

Fringe spacing decreases (interference fringes become closer together) as grating spacing increases and vice versa. It also decreases as the wavelength of light decreases.
The resolving power of a grating, or its ability to separate closely spaced frequencies, increases with more slits and higher orders.
The grating equation implies that diffraction grating can’t resolve wavelengths that differ by less than the wavelength of the light divided by the total number of slits.

Single-slit diffraction produces a broad central fringe with weaker, narrower fringes on either side. The pattern results from diffraction and resolution is limited.
Double-slit diffraction causes a similar interference pattern but with alternating diffraction and interference maxima. The narrower and brighter fringes result from two wave sources interfering.