To show that the second and third spectra of grating shone by wavelengths from 400 nm to 700 nm always overlap.

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Abagail Meyers · Accepted Answer

For second and third spectra to overlap, the diffraction angle for red light of the second-order spectra has to greater than the diffraction angle of violet light in the third order spectra.Write the formula for the condition of diffraction for second order spectra for red light.  d  sin  ⁡      θ          R      2        =  2      λ    R  Here, d is the grating spacing,       θ          R      2       is the diffraction angle for second order diffraction for red light       λ    R   is the wave length of red light.Write the formula for the condition of diffraction for third order spectra for violet light.  d  sin  ⁡      θ          V      3        =  3      λ    V  Here, d is the grating spacing       θ          R      2       is the diffraction for violet light       λ    V   is the wave length of violet light.Divide two equations:            d      sin      ⁡              θ                  R          2                            d      sin      ⁡              θ                  V          3                      =            2              λ        R                    3              λ        V                          sin      ⁡              θ                  R          2                            sin      ⁡              θ                  V          3                      =            2              λ        R                    3              λ        V            Substitute 700 nm for       λ    R  , 400 nm for       λ    V              sin      ⁡              θ                  R          2                            sin      ⁡              θ                  V          3                      =            2      (      700             n      m      )              3      (      400             n      m      )          =  1.166    &amp;gt;  1Thus the diffraction angle for red light of the second-order spectra has to greater than the diffraction angle of violet light in the third order spectra.

To show that the second and third spectra of wavelengths from 400 nm to 700 nm always overlap.

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