White light is spread out into its spectral components by a diffraction grating. If the grating has 2085 lines per centimeter, at what angle does red light of wavelength 640 nm appear in first-order spectrum?

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Jorge Franklin · Accepted Answer

Given in question: Number of slits(N) = 2085 lines/cm = 208500 lines/m  Wavelength  (  λ  )  =  640     n  m  =  640  ×      10          −      9           mOrder(n) = 1To find: Angle(  θ)Solution: Step1 - Calculating the grating constant(d).As we know, Grating spacing(d)   =  1  N  =  1208500  =  4.8  ×      10          −      6           mCalculating the angle(  θ).As we know that, grating condition is given by:   d  sin  ⁡  (  θ  )  =  n  λ  θ  =      sin          −      1        ⁡  (            n      λ        d    )  =      sin          −      1        ⁡  (            1      ×      640      ×              10                  −          9                            4.8      ×              10                  −          6                      )  θ  =      sin          −      1        ⁡  (  0.1333  )  =      7.66          ∘      Hence, the angle will be (      7.66          ∘      )

White light is spread out into its spectral components by a diffraction grating. If the grating has 2085 lines per centimeter, at what angle does red light of wavelength 640 nm appear in first-order spectrum?

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