Diffraction

What is Diffraction?

Diffraction is the bending of waves around the edges of an obstacle or aperture. It is a universal property of all waves — sound, water, light, and matter waves. For light, diffraction is not obvious in daily life because the wavelength of light (≈ 400–700 nm) is much smaller than the size of most objects we encounter.

However, diffraction becomes noticeable when light passes through a narrow slit or past a sharp edge. The shadow of an opaque object is not perfectly sharp; instead, near the edge of the geometrical shadow, you see alternating bright and dark fringes — similar to interference fringes. This is the signature of diffraction.

Why Diffraction Matters in Optics

• The finite resolution of the human eye and of optical instruments (telescopes, microscopes) is fundamentally limited by diffraction.
• The rainbow-like colours seen when light reflects off a CD or DVD are due to diffraction from the closely spaced grooves on the disc.

Key Idea: Huygens’ Principle and Diffraction

According to Huygens’ principle, every point on a wavefront acts as a source of secondary wavelets. When a wavefront encounters an obstacle or a slit, only a portion of the wavefront passes through. The secondary wavelets from the edges spread into the region of geometrical shadow, causing the wave to bend.

Single-Slit Diffraction (Fraunhofer Diffraction)

The most important case studied in NCERT Class 12 is Fraunhofer diffraction from a single slit. Here, the light source and the screen are effectively at infinite distances (plane wavefronts).

Consider a slit of width $a$ illuminated by monochromatic light of wavelength $\lambda$. The diffraction pattern on a distant screen consists of a central bright maximum flanked by alternating dark and bright fringes of decreasing intensity.

Condition for Minima (Dark Fringes)

The first minimum occurs when the path difference between light from the top and bottom edges of the slit equals one wavelength:

For the $n$th minimum (where $n = \pm 1, \pm 2, \pm 3, \dots$):

• $a$ = width of the slit
• $\theta_n$ = angular position of the $n$th minimum measured from the centre
• $\lambda$ = wavelength of light in the medium
• $n$ = order of the minimum (integer, excluding zero)

Condition for Maxima (Bright Fringes)

The maxima occur approximately midway between minima. The angular positions of the maxima are given by:

where $m = \pm 1, \pm 2, \pm 3, \dots$

Width of the Central Maximum

The central bright fringe extends from the first minimum on one side to the first minimum on the other side. Its angular width is:

$2\theta_1 = 2 \sin^{-1}\left(\frac{\lambda}{a}\right)$ …