# Diffraction grating

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In optics, a diffraction grating is an optical component with a periodic structure, which splits and diffracts light into several beams travelling in different directions. The directions of these beams depend on the spacing of the grating and the wavelength of the light so that the grating acts as the dispersive element. Because of this, gratings are commonly used in monochromators and spectrometers.

A photographic slide with a fine pattern of black lines forms a simple grating. For practical applications, gratings generally have grooves or rulings on their surface rather than dark lines. Such gratings can be either transmissive or reflective. Gratings which modulate the phase rather than the amplitude of the incident light are also produced, frequently using holography.

The principles of diffraction gratings were discovered by James Gregory, about a year after Newton's prism experiments, initially with artifacts such as bird feathers. The first man-made diffraction grating was made around 1785 by Philadelphia inventor David Rittenhouse, who strung hairs between two finely threaded screws. This was similar to notable German physicist Joseph von Fraunhofer's wire diffraction grating in 1821.

## Contents

### Theory of operation

The relationship between the grating spacing and the angles of the incident and diffracted beams of light is known as the grating equation.

According to the Huygens–Fresnel principle, each point on the wavefront of a propagating wave can be considered to act as a point source, and the wavefront at any subsequent point can be found by adding together the contributions from each of these individual point sources.

An idealised grating is considered here which is made up of a set of long and infinitely narrow slits of spacing d. When a plane wave of wavelength λ is incident normally on the grating, each slit in the grating acts as a point source propagating in all directions. The light in a particular direction, θ, is made up of the interfering components from each slit. Generally, the phases of the waves from different slits will vary from one another, and will cancel one another out partially or wholly. However, when the path difference between the light from adjacent slits is equal to the wavelength, λ, the waves will all be in phase. This occurs at angles θm which satisfy the relationship dsinθm/λ=|m| where d is the separation of the slits and m is an integer. Thus, the diffracted light will have maxima at angles θm given by