Diffraction

What is diffraction?

Diffraction is the spreading of wave energy into the space behind an obstacle when a wave passes the edge of that obstacle. Depending on the size of the obstacle compared to the wavelength, the wave may bend around it, reducing or eliminating the "shadow" region.

What happens when a wave encounters a small obstacle compared to its wavelength?

The wave energy passes around both sides of the obstacle, spreading into the space behind it. The obstacle produces little to no shadow, and the wavefront continues almost as if the obstacle were not there.

What happens when a wave encounters a large obstacle compared to its wavelength?

A shadow region forms behind the obstacle, but diffraction still occurs around the obstacle’s edges, allowing some wave energy into the shadowed area.

What happens when a wave passes through a narrow gap between two obstacles?

Diffraction occurs from each edge of the gap. The wave spreads out as it emerges, with maximum diffraction occurring when the gap width is approximately equal to the wavelength.

What factor primarily determines the amount of diffraction around an obstacle or through a gap?

The relationship between the wavelength of the wave and the size of the obstacle or gap. Diffraction is greatest when the gap width = wavelength.

Why can we hear around corners but not see around them?

Sound waves have wavelengths ranging from tens of cm to a few meters, which are similar in size to everyday obstacles like doors, allowing strong diffraction. Light waves, however, have much shorter wavelengths (~10-7 m), much smaller than obstacles, so they diffract negligibly and require direct line of sight.

Example: A doorway is about 1 m wide. What frequency of sound would have a wavelength equal to the doorway’s width, and why is this significant?

A sound with λ ≈ 1 m has f ≈ 330 Hz (speed of sound ≈ 330 m/s). This is within the human speech range, explaining why conversations can be heard around a doorway even if the speaker is not visible.

What is observed when light passes through a single narrow slit?

A diffraction pattern forms, with a bright, wide central maximum, surrounded by alternating dark regions (nodes) and smaller, dimmer bright fringes (antinodes). This results from interference of waves diffracted at the slit edges.

Why does a single-slit diffraction pattern have alternating bright and dark regions on the screen?

Waves from each edge of the slit interfere: In-phase → constructive interference → bright fringes. Out-of-phase → destructive interference → dark fringes. This creates an interference pattern of maxima and minima.

What happens to the diffraction pattern if the width of the slit is reduced?

Narrower slits produce wider diffraction patterns. The central maximum broadens, and the spacing between subsequent maxima and minima increases.

What is a diffraction grating?

A device consisting of a large number of parallel, equally spaced slits. When waves pass through, multiple diffraction patterns overlap, producing a precise interference pattern with regularly spaced bright and dark regions.

How is the diffraction grating equation written, and what does each symbol represent?

nλ = d sinθ ; n = order of maximum (integer, n=0 is central maximum), λ = wavelength of light, d = spacing between slits, θ = angle between central axis and nth bright fringe.

What does the central maximum correspond to in a diffraction grating pattern?

(n=0) is the bright fringe directly in line with the incident beam, at θ = 0.

Why are diffraction gratings useful in studying spectra?

Different wavelengths diffract at different angles according to nλ = d sinθ. This allows separation and precise measurement of wavelengths in light sources, making diffraction gratings essential in spectroscopy.