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When a particular line spectrum is examined using a diffraction grating of 300 lines {{mm}^{-1}} with the light at normal incidence, it is found that a line at {{24.46}^{\omicron }} contains both red (640–750 nm) and blue/violet (360– 490 nm) components. Are there any other angles at which the same thing would be observed?

Step-by-step

nλ = d sin θ = ({{10}^{-3}} m/300) sin {{24.46}^{\omicron }} = 1380 nm and the only possible values for n and λ to put the red and blue/violet light into the appropriate parts of the spectrum are {{n}_{R}} = 2, {{\lambda }_{R}} = 690 nm and {{n}_{BV}} = 3, {{\lambda }_{BV}} = 460 nm. In all physically possible cases nλ ≤ d sin {{90}^{\omicron }} = 3333 nm, and the only other pair of integers which are in the ratio 3m : 2m, with m less than (3333/1380) = 2.4, is 6 and 4. Thus there is only one more angle at which a two-component line will be observed; i.e. at {{sin}^{-1}}{\frac {(6*460)} {3333}}={{55.9}^{\omicron }}.

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