In -1 order, the free spectral range is λ 2/2, i.e. If λ 1 is the shortest wavelength and λ 2 is the longest wavelength in this wavelength interval, then the free spectral range may be expressed by:Įvidently the free spectral range is reduced when the grating is used in higher orders. The free spectral range of a grating is the largest wavelength interval in a given order which does not overlap the same interval in an adjacent order. When using gratings, it is therefore important to restrict the wavelength interval in some way, either by using a bandpass filter, or by making use of the limited wavelength range of the light source or the detector. By choosing a holographic grating with a high groove frequency, the instrument could be made more compact.Īs we can see from the grating equation, light of wavelength λ in the first order is diffracted in exactly the same direction as light of wavelength λ/2 in the second order, as well as λ/3 in the third order etc. The size of the instrument depends on the focal length of the optical system. If the focal length of the instrument is f, then the reciprocal linear dispersion is given by: The wavelength dispersion at the exit slit of a spectroscopic instrument is usually specified as reciprocal linear dispersion, given in nm/mm. Generally a fine pitch grating would be preferred because of the larger free spectral range (see below). High dispersion can be achieved either by choosing a grating with a high groove frequency, or by using a coarse grating in high diffraction order. An expression for the angular dispersion can be derived from the grating equation by differentiating, keeping the angle fixed. It is a measure of the angular separation between beams of adjacent wavelengths. The angular dispersion is the amount of change of diffraction angle per unit change of the wavelength. Two beams may also be combined at a grating surface. from a laser, a grating may be used as a beamsplitter, for generating two or more beams. Gratings with low groove frequency will generate many diffracted orders. The diffracted order with m = -1 is the order normally used in monochromators, spectrographs, and spectrometers. The reflected beam is the major cause of light losses in a grating. There will always be this solution and therefore a reflected beam, which usually is not wanted. λ= λ/n where λ = wavelength in vacuum, and n= refractive index.īy considering the case when m=0, the equation reduces to α=β 0 or the law of reflection. λ denotes the wavelength of the light in the medium surrounding the grating, usually air.The groove spacing in nanometers is then found by taking the reciprocal of the groove frequency, and multiplying by 10 6. Usually, gratings are specified by their groove frequency given as number of grooves per millimeter.
The angles are positive if they are directed counter clockwise, otherwise negative. The grating equation is a good starting point when describing the properties of gratings. The directions of these beams depend on the wavelength and direction of the incident beam, and on the groove frequency of the grating. Many of the most important spectroscopic properties, such as dispersion, resolution and free spectral range can be derived from the grating equation, from fairly straight forward algebraic manipulations.Ī beam of light which falls on a grating will be diffracted into one or several beams. The relation between the incidence and diffraction angles, and the wavelength is given by the well known grating equation. This is achieved by utilizing the grating’s ability of spreading light of different wavelengths into different angles. Diffraction gratings are widely used in spectroscopic instruments, for creating monochromatic light from a white light source.
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