White light is spread out into its spectral components by a diffraction grating. if the grating has 2 010 grooves per centimeter, at what angle does red light of wavelength 640 nm appear in first order

The applicable expression is:

Sin Ф = Wavelength/Grating spacing

Where,

Ф = Angle of red light

Wavelength = 640 nm = 640*10^-9 m

Grating spacing = 1 cm/2010 = 0.01/2010 = 4.975 * 10 ^-6 grooves per meter

Therefore,

Ф = Sin ^-1 [ (640*10^-9) / (4.975*10^-6) ] = 7.39°