Light of wavelength 650 nm is normally incident on the rear of a grating. The first bright fringe (other than the central one) is at an angle of 5o with respect to the normal. A. Find the number of slits per centimeter in the grating.
B. Two rays of light of wavelength 650 nm and 420 nm are normally incident on a different grating. If the grating has 5000 slits/cm, what is the angular seperation of of the two light rays' second order maximum?

A

B

Explanation:

From the question we are told that  

      The wavelength is    

        The angle of  first bright fringe is    

        The order of the fringe considered is  n  =1

Generally the condition for constructive interference is  

=>    

=>    

Converting to cm

Generally the number of grating pre centimeter is  mathematically represented as

=>        

=>        

Considering question B  

   From the question we are told that

     The first wavelength is  

     The second wavelength is  

      The order of the fringe is  

       The grating is  

Generally the slit width is mathematically represented as

=>          

=>          

Generally the condition for constructive interference for the first ray is mathematically represented as

=>      

=>      

=>        

Generally the condition for constructive interference for the second ray is mathematically represented as

=>      

=>      

=>        

Generally the angular separation is mathematically represented as

=>          

=>          

1/0.14nm = 10^10/1.4 a lot

double the distance = divide strength by 4