(a) In Young's double slit experiment, describe briefly how bright and dark fringes are obtained on the screen kept in front of a double slit. Hence obtain the expression for the fringe width.

(b) The ratio of the intensities at minima to the maxima in the Young's double slit experiment is 9: 25. Find the ratio of the widths of the two slits.

a)
Let S₁ and S₂ be two coherent sources separated by a distance d.

Let the distance of the screen from the coherent sources be D. Let point M be the foot of the perpendicular drawn from O, which is the midpoint of S₁ and S₂ on the screen. Obviously point M is equidistant from S₁ and S₂. Therefore the path difference between the two waves at point M is zero. Thus the point M has the maximum intensity.

Now, Consider a point P on the screen at a distance y from M. Draw S₁N perpendicular from S₁ on S₂ P. 

The path difference between two waves reaching at P from S₁ and S₂ is given by, 
 
Since, D >> d, so  is very small.
 
  

For dark fringe, path difference is an odd multiple of half wavelength.
So, we have  
 

Let, be the distance of two consecutive fringes. Then, we have
 

Fringe width is same for both bright and dark fringe.

b)
Give, ratio of minima to maxima intensity is given by, 9:25

That is,