Question

When a student shines a 540 nm laser through this grating, how many bright spots could be seen on a screen behind the grating?

Answer 1

Complete Question

A commercial diffraction grating has 600 lines per mm.  

When a student shines a 540 nm laser through this grating, how many bright spots could be seen on a screen behind the grating?

Answer:

The number of  bright spots is  $m = 7$    

Explanation:

From the question we are told that

  The wavelength is  $\lambda = 540 nm = 540 *10^{-9} \ m$

   The number of lines per length the commercial diffraction grating has is $L = 600 \ lines / mm = 600 * 1000 \ lines / m = 600 *10^{3} \ lines / m$

Generally the condition for constructive interference is mathematically represented as

       $dsin(\theta) = n\lambda$

Here d  is the separation between the gratings which is mathematically represented as

       $d=\frac{1}{L}$

=>    $d=\frac{1}{600 *10^{3}}$

=>    $d= 1.67 *10^{-6 } \ m$

and  n is the order of bright fringe, the maximum number is seen when $\theta = 90^o$

So

   $1.67 *10^{-6}sin(90) = n * 540 *10^{-9 }$

=>  $n = 3$

Generally the number of bright spot (considering central bright fringe and the same order of bright fringe on each side of the central  bright fringe) is mathematically represented as

      $m = n * 2 + 1$

=>   $m = 3 * 2 + 1$

=>   $m = 7$