Question

For a single slit of width `a`, the first minimum of diffraction pattern of a monochromatic light of wavelength `lambda` occurs at an angle of `lambda//a`. At the same angle of `lambda//a`, we get a maximum for two narrow slits separated by a distance a. Explain.

Answer 1

In the interference pattern due to narrow slits separated by distance `a`, path differecne `= a sin theta`. For constructive interference, `a sin theta = 1 lambda, sin theta ~= theta = lambda//a`, we get a maximum. In the diffraction pattern due to a single slit, when path difference from secondary waves from the ends of wavefront is `lambda`, then for every point in one half of the lower half for which path diff. between secondary waves is `lambda//2`. Therefore, interference is destructive and we obtain first minimum at the same angle.