Spectral Lines Overlapping
If the light incident on the grating surface consists of a large range of wavelengths, then the spectral lines of shorter wavelength and of higher order overlap on the spectral lines of longer wavelength and of lower order. Let the angle of diffraction θ be the same for (i) the line of wavelength λ1 in the first order, (ii) the spectral line of wavelength λ2 in the third order. Then
(a + b) sin θ = 1.λ1 = 2.λ2 = 3.λ3 = …….
The red line of wavelength 7000 Å in the third order, the green line of wavelength 5200 Å in the fourth order and the violet line of wavelength 4200 Å in the fifth order are all formed at the same position of the screen because,
(a + b) sin θ = 3 × 7000 × 10-8
= 4 × 5250 × 10-8
= 5 × 4200 × 10-8
Here (a + b) is expressed in cm.
For the visible region of the spectrum, there is no overlapping of the spectral lines. The range of wavelengths for the visible part of the spectrum is 4000 Å to 7000 Å. Thus, the diffracting angle for the red end of the spectrum in the first order is less than the diffracting angle for the violet end of the spectrum in the second order. If, however, the observations are made with a photographic plate, the spectrum recorded may extend up to 2000 Å in the ultraviolet region. In this case, the spectral line corresponding to a wavelength of 4000 Å in the first order and a spectral line of wavelength 2000 Å in the second order overlap. Suitable filters are used to absorb those wavelengths of the incident light which will overlap with the spectral lines in the region under investigation.
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