Question

Find the angles of the first three principal maxima above the central fringe when this grating is illuminated with 672 nm light.

Answer 1

Complete Question

A grating has 767 lines per centimetre.Find the angles of the first three principal maxima above the central fringe when this grating is illuminated with 672 nm light.

Answer:

The  first is  

      $\theta_1 = 2.92^o$

 The second is  

       $\theta _2 = 5.93^o$

 The third is  

        $\theta _3 = 8.92^o$

Explanation:

From the question we are told that

        The  number of lines per cm is  $I = 767 \ lines/cm = 76700 \ lines / m$

        The  wavelength is  $\lambda = 672nm = 672 *10^{-9} \ m$

       

Generally the condition for constructive  interference is  

            $dsin (\theta ) = n\lambda$    

Here d is the distance of separation of the slit which is mathematically represented as

             $d = \frac{1}{l}$

             $d = \frac{1}{76700}$

             $d = 1.30*10^{-5} \ m$

So          

           $\theta_1 = sin^{-1} [\frac{ n \lambda }{ d} ]$

For the  first angle  n =  1  

  So  

        $\theta_1 = sin^{-1} [\frac{ 1 * 672 *10^{-9} }{ 1.30 *10^{-5}} ]$

          $\theta_1 = 2.92^o$

For  the second angle  n  =  2

      So  

            $\theta_2 = sin^{-1} [\frac{ 2 * 672 *10^{-9} }{ 1.30 *10^{-5}} ]$

            $\theta _2 = 5.93^o$

For  the second angle  n  =  3

      So  

           $\theta_3 = sin^{-1} [\frac{ 3 * 672 *10^{-9} }{ 1.30 *10^{-5}} ]$

          $\theta _3 = 8.92^o$