question_answer

In YDSE distance between the \[{{S}_{1}}\]and\[{{S}_{2}}\]is d. \[{{P}_{1}}\]and\[{{P}_{2}}\]are two points equidistance from O at an angular position \[\beta \]as shown. A parallel beam of monochromatic light is incident at an angle a on the slits. Then the ratio of path difference at\[{{P}_{1}}\]and\[{{P}_{2}}\]is:

A) \[\cot \frac{\alpha -\beta }{2}\cot \frac{\alpha +\beta }{2}\]         

B) \[\tan \frac{\alpha +\beta }{2}\cot \frac{\alpha -\beta }{2}\]

C) \[\sin \frac{\alpha +\beta }{2}\cos \frac{\alpha -\beta }{2}\]          

D) \[\tan \frac{\alpha -\beta }{2}\cot \frac{\alpha +\beta }{2}\]