Question

A parallel beam of monochromatic light falls normally on a single slit of width ‘a’ and a diffraction pattern is observed on a screen placed at distance D from the slits. Explain:

1. the formation of maxima and minima in the diffraction pattern, and
2. why the maxima go on becoming weaker and weaker with its increasing number (n).

Answer 1

I. Consider a slit of width a. If the path difference between light from the top and bottom of the slit is:

a sin θ = nλ (n = 1, 2, 3, ...)

Then, the waves cancel pairwise by destructive interference, giving dark fringes.

Thus, the condition for minima:

a sin θ = nλ

Between successive minima, waves interfere constructively to give bright regions. The central maximum occurs at θ = 0, where all wavelets are in phase. Secondary maxima occur between minima due to partial constructive interference.

II. Higher-order maxima become weaker because:

1. As angle θ increases, path differences across the slit increase.
2. Contributions from different parts of the slit increasingly cancel each other
3. Only partial constructive interference occurs.
4. Energy spreads over a wider angular region.