Diffraction gratings with 10,000 lines per centimeter are readily available. Suppose you have one, and you send a beam of white light through it to a screen 2.00 m away.Find the angles for the first-order diffraction of the shortest and longest wavelengths of visible light (380 and 760 nm).

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Sanaa Hudson · Accepted Answer

Given information:The number of lines on the grating,   N  =  10000   lines/cm  =  10000  ×      lines                  10                  −          2                     m        =      10    6     lines/mThe distance between the screen and slits,   D  =  2.00   mThe shortest wavelength,       λ          min        =  380   nm  =  380  ×      10          −      9         mThe longest wavelength,       λ          max        =  760   nm  =  760  ×      10          −      9         mTo find the angles corresponding to first-order diffraction from these wavelengths. The grating equation is given by  d  sin  ⁡  (  θ  )  =  n  λ    sin  ⁡  (  θ  )  =            n      λ        d      θ  =      sin          −      1        ⁡            n      λ        d  where,d=width of the slitn=order of diffraction  λ  = wavelength of incident light  θ  = angle of diffractionThe width of the slit is calculated as follows  d  =      1    N      d  =      1          10      6          d  =      10          −      6         mApply the above formula for the shortest wavelength      θ          min        =      sin          −      1        ⁡  (            1      ×      380      ×              10                  −          9                            10              −        6              )    =      sin          −      1        ⁡  (  0.38  )    =      22.33    ∘  Now, apply the above formula for the longest wavelength      θ          max        =      sin          −      1        ⁡  (            1      ×      760      ×              10                  −          9                            10              −        6              )    =      sin          −      1        ⁡  (  0.76  )    =      49.46    ∘  Answer:The angle corresponding to the shortest wavelength is,       θ          min        =      22.33    ∘  The angle corresponding to the longest wavelength is,       θ          max        =      49.46    ∘

Diffraction gratings with 10,000 lines per centimeter are readily available.

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