Diffraction Grating

Question

Light is shone on a diffraction grating with d=2.25*10^-6 m. The first order (m=1) maximum occurs at an angle of 15.7 deg. What is the wavelength of the light in nanometers? 

Answer 1

mλ = d sinθ

m = 1

d = 2.25 x 10^-6 m

θ = 15.7°

λ = (2.25 x 10^-6 m) sin(15.7°) ≅ 6.089 x 10^-7 m = 608.9 nm