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Thermodynamics

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Prism and Grating Spectra

For dispersing a given beam of light and for studying the resultant spectrum, a diffraction grating is mostly used instead of a prism.

The following points give broadly the distinction between the spectra obtained with a grating and a prism.

(i) With a grating, a number of spectra of different orders can be obtained on the two sides of the central maximum whereas with a prism only one spectrum can be obtained.

(ii) The spectra obtained with a grating are comparatively pure than those with a prism.

(iii) Knowing the grating element (a + b) and measuring the diffraction angle, the wavelength of any spectral line can be measured accurately. But in the case of a prism the angles of deviation are not directly related to the wavelength of the spectral line. The angles of deviation are dependent on the refractive index of the material of the prism, which depends on the wavelength of light.

(iv) With a grating, the diffracting angle for violet end of the spectrum is less than for red. In fig. V₁R₁ and V₁’R₁’ refer to the first order spectra on the two sides of the central maximum P. With a prism, the angle of deviation for the violet rays of light is more than for the red rays of light.

(v) The intensities of the spectral lines with a grating are much less than with a prism. In a grating spectrum, most of the incident light energy is associated with the undispersed central bright maximum and the rest of the energy is distributed in the different order spectra on the two sides of the central maximum. But in the prism, most of the incident light energy is distributed in a single spectrum and hence brighter spectral lines are obtained.

(vi) The dispersive power of a grating is given by

and this is constant for a particular order. Thus, the spectral lines are evenly distributed. Hence, the spectrum obtained with a grating is said to be rational. The refractive index of the material of a prism changes more rapidly at violet then at the red end of the spectrum. The dispersive power of a prism is given by and this has higher value in the violet region of the spectrum than in the red region. Hence, there will be more spreading of the spectral lines towards the violet and spectrum obtained with a prism said to be irrational.

(vii) The resolving power of a grating is given by nN where n is the order of the spectrum and N is the total number of lines on the grating surface. The resolving power of a prism is given by t where t is the base of the prism and is the rate of change of refractive index with wavelength. The resolving power of a grating is much higher than that of a prism. Hence the same two nearby spectral lines appear better resolved with a grating than with a prism.

(viii) Lastly, the spectra obtained with different gratings are identical because the dispersive power and the resolving power of grating do not depend on the nature of the material of the grating. But the spectra obtained with different prisms are never identical because both dispersive power and the resolving power of a prism depend on the nature of the material of the prism.