Light of a single wavelength is incident on a diffraction grating with 500 slits

Question

Light of a single wavelength is incident on a diffraction grating with

500 slits/mm. Several bright fringes are observed on a screen behind the grating, including one at 47.3 and one next to it at 78.5 .

Problem 17.57 Light of a single wavelength is incident on a diffraction grating with 500 slits/mm. Several bright fringes are observed on a screen behind the grating, including one at 47.3 ° and one next to it at 78.5 Part A What is the wavelength of the light? Express your answer with the appropriate units. Value Units Submit My Answers Give Up

Explanation / Answer

gIVEN

  
diffraction grating with 500 slits permm

so the slit width is = 0.01/500 m = 2*10^-5 m

the bright fringes are formed on the screen at47.3 degrees and second at 78.5 degrees

from the formula of grating

       d sin theta = m*Lambda

   d sin (thet2 - theta1) = m *lambda

  

   lambda = d sin (theta2-theta1)/m

       = 2*10^-5 sin (78.5-47.3)

here the angle converted in to radians and solving for lambda

       = (4.28505)*10^-6 m

       = 4285.05 nm

the wavelength of the light is lambda = 4285.05 nm

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