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Find the total number of lines in a 2.5-cm-wide diffraction grat- ing whose third-order spectrum puts the 656-nm hydrogen-a spectral line 37° from the central maximum.

Find the total number of lines in a 2.5-cm-wide diffraction grat- ing whose third-order spectrum puts the 656-nm hydrogen-a spectral line 37° from the central maximum.

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Find the total number of lines in a 2.5-cm-wide diffraction grat- ing whose third-order spectrum puts the 656-nm hydrogen-a spectral line 37° from the central maximum.
Transcribed Image Text:Find the total number of lines in a 2.5-cm-wide diffraction grat- ing whose third-order spectrum puts the 656-nm hydrogen-a spectral line 37° from the central maximum.
Expert Solution
Concept and Principle:
  • A diffraction grating in optics is used to diffract light into several beams in different directions. It consists of multiple lines or slits which cause constructive interference and a diffraction spectrum is formed.

 

  • The condition for constructive interference is given by,

    dsinθ=mλ

    Here d is the slit width, θ is the angular position, m is the order of the fringe, and λ is the wavelength

 

  • The number of lines will be given by,

n=Ld

Here L is the length of the grating and d is the slit width.

 

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