Pure and Impure Spectrum | Angular Dispersion | Physics Grade XI

Pure and Impure Spectrum

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Refraction Through Prisms

Pure and Impure Spectrum | Angular Dispersion | Physics Grade XI

Pure and Impure Spectrum | Angular Dispersion

Pure and Impure spectrum
A collection of dispersed light which gives its wavelength composition is called spectrum. After dispersion, if the splitted rays overlap with each other and all the colors cannot be seen clearly, then that type of spectrum is called an impure spectrum. Impure spectrum has different colors at small region.
Impure Spectrum

Pure spectrum: After dispersion, if the splitted rays do not overlap with each other and all the colors can be seen distinctly, then the spectrum is called pure spectrum. Pure spectrum has single color at small region.

Pure Spectrum

Angular Dispersion
When a beam of light passes through a prism, light of different colors is deviated by different amounts. The mean deviation of light is measured by the deviation of yellow light as its deviation is nearly the average of all deviation. As shown in the figure, the red light is least deviated and the violet light is the most deviated. The angular dispersion is calculated as the angle between the least deviated and the most deviated.
Angular dispersioni.e; angular dispersion = δv – δr ……... (i)
since the deviation for small angle prism is δ = A (µ - 1), then
deviation for violet light, δv = A (µv – 1)
and deviation for red light, δr = A (µr – 1)
then equation (i) becomes,
angular dispersion = δv – δr
                           = A (µv – 1) - A (µr – 1)
                           = A (µv - µr)
 
Dispersive Power
Dispersive power of a prism is defined as the ratio of angular dispersion to the deviation of mean color.
 
Disperive power, ω = (δv – δr)/ δ
                            = {A (µv – 1) - A (µr – 1)} / A (µ-1)
Here, δ = A (µ-1) is the angle of deviation for mean color
Then, ω = A (µv - µr) / A (µ-1)
      .: ω = (µv - µr)/ (µ-1)

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