Diffraction grating as a spectral instrument

The most important characteristics of the quality of a spectral device are dispersion D and resolution R. Distinguish an angular and hnear dispersion. The value numerically equal to the ratio of the angular distance between spectral lines d(p to the difference of wavelengths 5X of these spectral lines is referred to as angular dispersion. The angular dispersion is equal 

In order to obtain an expression for angular dispersion, we should find a derivative dcpidk from eq. (6.3.4) and change further the differentials into finite increments (neglecting the minus sign). At small angles, eq. (6.3.4) can be rewritten as b(p = mk and then 

Linear dispersion is the value numerically equal to the ratio of the linear distance in the spectrum between the spectral lines 51 to the difference 5 k corresponding to those hnes 

Another device that permits the decomposition of incident radiation in the spectrum is a prism. Decomposition in the spectrnm by a prism is dne to the dependence of the angle of refraction on the wavelength. The corresponding formnla for the prism can be obtained nsing expression (6.1.2). Notice that the sign of the derivative dcpIdX for the diffraction grating and for the prism is different. 

It can be seen that the resolving power is larger when a longer grating length and higher order reflections are used. 

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