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

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?

The number of  bright spots is      

Explanation:

From the question we are told that

  The wavelength is  

   The number of lines per length the commercial diffraction grating has is

Generally the condition for constructive interference is mathematically represented as

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

=>    

=>    

and  n is the order of bright fringe, the maximum number is seen when

So

=>  

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

=>  

=>