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Monochromatic light from a helium-neon laser of wavelength of 632.8 nm is incident normally on a diffraction grating containing 6000 lines/cm. Find the angles at which one would observe the first order maximum, the second-order maximum, and so forth.

Respuesta :

Answer:

first-order maximum:\theta=sin^{-1}(0.10533*10^{-11}  )

second-order maximum:\theta=sin^{-1}(2.1066*10^{-11}  )

Step-by-step explanation:

  • here, maximum means bright fringes
  • FORMULA :for bright fringes, we know that dsin[tex]\theta[/tex]=n[tex]\lambda[/tex]

(refer the diagram uploaded in the attachment)

  • here,[tex][tex]\lambda= 632.8*10^{-9} meters \\d=6000*10^{2} lines/meter[/tex]
  • for first order maximum, n=1

by substituting these values in the above formula,

[tex]sin\theta=\frac{1*632*10^{-9} }{6000*10^{2} } \\ =0.10533*10^{-11} \\therefore, \theta=sin^{-1}(0.10533*10^{-11}  )\\[/tex]

  • for second order maximum, n=2

[tex]sin\theta=\frac{2*632*10^{-9} }{6000*10^{2} } \\ =2*0.10533*10^{-11} \\therefore, \theta=sin^{-1}(2.1066*10^{-11}  )[/tex]

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