If white light illuminates a diffraction grating having 690 lines/mm, over what range of angles does the visible m = 1 spectrum extend?

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Physics

Leonie

1 April, 02:13

If white light illuminates a diffraction grating having 690 lines/mm, over what range of angles does the visible m = 1 spectrum extend?

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Deegan Barry · Answer 1

Human eye is capable of detecting wavelengths between 400 nm and 700 nm.

Sin Ф = wavelength/distance between lines

Distance between lines (d) = 1/690 = 1.445*10^-3 mm = 1.445*10^-6 m

Angle at 400 nm: SinФ = (400*10^-9) / (1.445*10^-6) = 0.276 = > Ф=Sin^-1 (0.276) = 16.02°

Angle at 700 nm: Sin Ф = (700*10^-9) / (1.445*10^6) = 0.484 = > Ф=Sin^-1 (0.484) = 28.97°

Range of angles: 16.02° to 28.97°