Coherent electromagnetic waves with wavelength l pass through a narrow slit of width a. The diffraction pattern is observed on a tall screen thatis 2.00 m from the slit. When l = 500 nm, the width on the screen of thecentral maximum in the diffraction pattern is 8.00 mm. For the same slit and screen, what is the width of the central maximum when l = 0.125 mm?

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This is a problem based on diffraction of light . Case: 1When the wavelength,   λ  =  500     n  m  =  500  ×      10          −      9           mTotal linear width of the central maxima   =  8.00   mm  =  8  ×      10          −      3         mHalf linear width of central maxima,   s  =  4  ×      10          −      3         mdistance of the screen from the slit, D=2.00 mHalf Angular width   =  θ  θ  =      λ    a  where a is the slit width of the system  s  =  D  θ    s  =            λ      D        a      a  =            λ      D        s    =            500      ×              10                  −          9                    ×      2              4      ×              10                  −          3                      =  2.5  ×      10          −      4      Now we consider for the 2nd case. Case : 2Wavelength used,   λ  =  0.125   mm  =  0.125  ×      10          −      3         m    a  =  2.5  ×      10          −      4         mangular half width,   θ  =      λ    a    =            0.125      ×              10                  −          3                            2.5      ×              10                  −          4                      =  0.5linear half width,       s    ′    =  θ  D  =  0.5  ×  2  =  1   mtotal linear width of the central maximum,   2      s    ′    =  2  ×  1  =  2   mAnswer: total width of the maximum =2 m

For the same slit and screen, what is the width of the central maximum when l = 0.125 mm?

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