Question

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

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°