9.3 Diffraction of Waves

Diffraction is the phenomenon observed when waves encounter an obstacle or an aperture (a slit). It is characterized by the bending of waves around the corners of the obstacle or slit and their subsequent spreading into the region of the geometrical shadow. This effect is a hallmark of all types of waves, including sound, water, and light waves.

The Principle of Diffraction

When a wavefront passes through a narrow opening or past a sharp edge, every point on that portion of the wavefront acts as a source of secondary spherical wavelets (Huygens' Principle). These wavelets spread out in all directions and interfere with each other, creating a new wavefront that is different from the original. This interference pattern is what we observe as diffraction.

Conditions for Significant Diffraction

Diffraction is always occurring, but it is only noticeable under specific conditions:

• The most prominent diffraction occurs when the size of the obstacle or aperture ($d$) is comparable to the wavelength ($\lambda$) of the wave.
• If $d\gg \lambda$, the waves pass by with very little bending and the effect is negligible — the wave travels mostly in straight lines.

Diffraction in Water Waves

The diffraction of water waves is easily observable in a ripple tank.

• When plane water waves pass through a narrow slit (slit width $\approx \lambda$), the waves emerge as semicircular wavefronts, spreading out in all directions.
• If the slit is made much wider than the wavelength, the waves pass through mostly unchanged, with only slight bending at the edges.

Diffraction of Light Waves

Because the wavelength of visible light is extremely small (approximately $400\text{–}700\text{ nm}$), diffraction of light is not commonly observed in everyday life — it requires very small obstacles or slits.

Single-Slit Diffraction

When monochromatic light passes through a very narrow single slit and is projected onto a screen, a characteristic diffraction pattern is observed:

• A central bright fringe that is much wider than the slit itself, with the highest intensity.
• A series of alternating dark and bright fringes on either side of the central fringe.
• The intensity of the side bright fringes decreases rapidly with distance from the centre.

The dark fringes correspond to points of complete destructive interference between wavelets from different parts of the slit.

Diffraction Grating

A diffraction grating is an optical component consisting of a large number of close, parallel, equally spaced slits (rulings) on a glass plate. It splits and diffracts light into beams travelling in specific directions.

The Grating Equation for principal maxima is:

$d\sin \theta =n\lambda$

where:

• $d$ = grating element (distance between adjacent slits)
• $\theta$ = angle of diffraction
• $n$ = order of the maximum ($n=0,1,2,\dots$)
• $\lambda$ = wavelength of light

X-Ray Diffraction

Since X-rays have very short wavelengths (comparable to inter-atomic spacing in crystals), they can be diffracted by the regular arrangement of atoms in a crystal lattice. This is described by Bragg's Law:

$2d\sin \theta =n\lambda$

where $d$ is the inter-planar spacing. X-ray diffraction is used to study the internal atomic structure of crystals.

Why Can We Hear Around Corners But Not See?

This is a classic example of diffraction. The wavelength of sound waves (centimetres to metres) is comparable to the size of everyday obstacles like doorways and corners, so sound diffracts easily around them. The wavelength of light is extremely small ($\sim 10^{-7}\text{ m}$), so it does not diffract noticeably around large obstacles and travels in essentially straight lines.

Diffraction vs. Interference

Summary Table