Question

Discuss diffraction at single slit and obtain the condition for n^th minimum.

Answer 1

1. Let a parallel beam of light fall normally on a single slit AB of width. The diffracted beam falls on a screen kept at a distance. The center of the slit is C. A straight line through C perpendicular to the plane of slit meets the center of the screen at O.
2. All the waves start parallel to each other from different points of the slit and interfere at point P and other points to give the resultant intensities. The point P is in the geometrically shadowed region, up to which the central maximum is spread due to diffraction. 

• Condition for P to be first minimum:

1. Let us divide the slit AB into two half’s AC and CB. Now the width of AC is (a/2). They are called corresponding points.
2. The path difference of light waves from different corresponding points meeting at point P and interfere destructively to make it first minimum.
3. The path difference δ between waves from these corresponding points is,
   δ = `"a"/2 sin theta`
   The Condition for P to be first minimum,
   `"a"/2  sin theta = lambda/2`
   

   a sin θ = λ (first minimum)

• Condition for P to be n^th order minimum:
  Dividing the slit into 2n number of (even number of) equal parts the condition for n^th order minimum is
  `"a"/"2n"` sin θ = `λ/2`
  a sin θ = nλ (n^th minimum)
  
  Diffraction at single slit
  
  Corresponding points