Question

Light shines through a single slit whose width is 5.6 × 10-4 m. A diffraction pattern is formed on a flat screen located 4.0 m away. The distance between the middle of the central bright fringe and the first dark fringe is 3.3 mm. What is the wavelength of the light?

Answer 1

From the relation of the diffraction minima condition
   
And so, for the first dark fringe, m = 1. And so,
  
where, d is the slit width.
And if the distance between the slit and the screen is D and the distance of the first dark fringe from the center of the central bright fringe is y_1, then, we have
  
Now in the limit
  
we can approximate
   
And so, we have from the diffraction mimnima condition for m = 1,
  
  
And so, putting the given values, we get