A diffraction grating having 500 lines/mm diffracts visible light at 30°. What is the light's wavelength?

The light's wavelength is 500 nm

Explanation:

mλ = d*sin (θm)

where;

λ is the visible light wavelength (nm) = ?

d is the groove (slit) spacing (mm/lines) = 1/500mm

θm is the angle of refraction

m is is the diffraction order, for visible light range, m = 2

λ = [d*sin (θm) ]/m

λ = (sin30) / (500*2) = (0.5) / (1000) = 0.0005 mm = 500 nm

Therefore, for a diffraction grating having 500 lines/mm and diffracts visible light at 30°. The light's wavelength is 500 nm