10.5.3 Diffraction

When a sound wave passes through an opening, it spreads outward. When a water wave passes the edge of a breakwater, it spreads inward. The spreading of waves (into the so-called geometric shadow) when they pass through an opening or around an obstacle is called diffraction.

The degree of spreading depends on the width of the opening or obstacle relative to the wavelength (of the wave).

Light Waves

We have already discussed the diffraction of light extensively; the single slit interference is the diffraction of light (after passing through a slit). The diffraction grating is called a diffraction grating because the slits are so narrow that light diffracts extensively after passing through it.

Light waves have very short wavelength (<750 nm for visible light). So even a 1 mm slit would be too wide to cause any appreciable spreading in the emergent beam. (Think \displaystyle \sin {{\theta }_{1}}=\frac{\lambda }{b}). The first minima angle is practically zero, meaning no spreading). This is why the diffraction of light usually requires a careful and deliberate setup before they are observable.

Other Waves

Sound waves and water waves have wavelengths ranging from centimeters to meters. So the diffraction of sounds waves and water waves as they interact with common objects are much more readily observable.

The following are typical illustrations of diffraction, found in many textbooks. Strictly speaking, they are what I call artists’ impressions of the diffraction phenomena because the actual picture is a lot more complicated. Even though diffraction (through an opening) is fundamentally single-slit interference, the single-slit formula we derived earlier are not accurate for these drawings. This is because we are too near the slit for the simplification offered by the parallel-ray approximation to be valid.

Nevertheless, the main idea is that the degree of spreading depends on the width of the slit (or obstacle) relative to the wavelength. The narrower the slit and the longer the wavelength, the more the spreading. In the extreme case where the slit has negligible width compared to the wavelength, the wave energy is spread (almost) uniformly in all directions (thus behaving like a point source).

Applets

How wavelength and slit/obstacle width affect Diffraction (ngsir)

Concept Test

2045

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