Question

Why did we use \[\lambda\] as the path difference between the waves originating from extreme points for the first minimum?

Answer 1

For the first minimum in single-slit diffraction, the path difference between the extreme rays is taken as \[\lambda\]. The slit can then be divided into two equal halves. Each point in one half has a corresponding point in the other half, and the path difference between each pair is \[\frac{\lambda}{2}\]. Hence, every pair produces destructive interference, giving the first minimum.