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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

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jushmk
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°

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