Diffraction
Section: Superposition | Syllabus: Cambridge AS Level Physics 9702
What is Diffraction? Waves travel in straight lines when unobstructed. When waves pass the edge of an obstacle or pass through a gap between obstacles, they spread out. This spreading of waves is called diffraction .
Diffraction The spreading out of waves when they pass the edge of an obstacle or pass through a gap between obstacles into regions of geometrical shadow. Universal Property Diffraction occurs for all wave types: water waves, sound, light, microwaves, and other EM waves.
It requires only a single wave source-coherence is not needed. Huygens' Explanation Every point on a wavefront acts as a secondary source of wavelets. The new wavefront is the sum of these wavelets. At a gap, only the points within the gap act as sources, causing the wave to spread out.
FIG 8.11: Huygens' Construction for Diffraction Show: incident plane wavefront approaching a gap in a barrier, secondary sources (dots) within the gap, curved wavelets emanating from each secondary source, resulting diffracted wavefront spreading into the geometrical shadow region.
Label the shadow areas on either side of the direct path. Conditions Affecting Diffraction The extent of diffraction depends on the ratio of wavelength to gap width (or obstacle size). FIG 8.12: Diffraction Through Different Gap Widths Show three cases using wavefronts: (a) λ > a (gap much smaller): very little transmission.
Label λ (wavelength), a (gap width), and direction of wave travel. Effect of Gap Width Gap >> wavelength: Slight diffraction at edges only; wavefronts remain mostly straight Gap ≈ wavelength: Maximum diffraction; waves spread into semicircular pattern Gap Very little wave passes through; mostly reflected Maximum Diffraction Condition: Maximum spreading occurs when: gap width wavelength i.e., when a λ where: a = gap width (m) λ = wavelength (m) Effect of Wavelength For a fixed gap width: Longer wavelength: Greater diffraction (more spreading) Shorter wavelength: Less diffraction (less spreading) Why This Matters This explains why we can hear sounds around corners (sound has wavelengths of metres, comparable to doorway widths) but cannot see around corners (light has wavelengths of nanometres, much smaller than typical gaps).
Diffraction Around Obstacles Diffraction also occurs when waves encounter an obstacle. The waves bend around the edges of the obstacle and partially enter the "shadow" region behind it. The amount of bending depends on the ratio of wavelength to obstacle size Maximum diffraction around an obstacle occurs when the obstacle size is comparable to the wavelength Large obstacles (compared to wavelength) cast sharp shadows with minimal diffraction Experimental Demonstrations of Diffraction 1.
Water Waves in a Ripple Tank Plane waves generated by a rectangular paddle are directed towards a barrier with an adjustable gap. FIG 8.13: Ripple Tank Diffraction Show two scenarios: (a) Wide gap (a >> λ): plane wavefronts passing through with slight edge curvature, (b) Narrow gap (a ≈ λ): waves spreading out in semicircular pattern.
Label: incident plane waves, gap width a, diffracted waves, geometrical shadow regions. Observations: Wide gap: Wavefronts remain mostly straight; slight curving at edges only Narrow gap (≈ λ): Waves spread into semicircular pattern; gap acts as point source Wavelength unchanged by diffraction 2.
Diffraction of Light Through a Single Slit Monochromatic light (e.g., laser) passes through a narrow slit onto a distant screen. FIG 8.14: Single-Slit Diffraction Pattern Show: laser → narrow slit → screen.
On screen, show intensity pattern: wide, bright central maximum, then alternating dark minima and progressively dimmer secondary maxima on both sides. Include intensity vs position graph below showing the characteristic pattern with central peak much wider and taller than side peaks.
Observations: Central maximum: widest and brightest Secondary maxima: progressively dimmer, narrower Dark minima (destructive interference) between maxima Pattern is symmetrical Effect of slit width: Narrower slit: More spreading; central maximum wider Wider slit: Less spreading; central maximum narrower Wave Evidence Single-slit diffraction demonstrates the wave nature of light.
Particles would not spread into shadow regions. 3. Sound Diffraction Around Obstacles Sound waves diffract readily because their wavelengths (typically 0.017 m to 17 m for audible sound) are comparable to everyday objects and gaps.
Observations: You can hear sounds around corners and through doorways even when you cannot see the source Lower frequency (longer wavelength) sounds diffract more than higher frequency sounds Bass notes spread around obstacles more effectively than treble notes Practical example: When music is playing in another room, you may hear the bass notes more clearly than the treble notes through a partially open door, because the longer wavelength bass sounds diffract more around the door edge.
Diffraction Pattern Intensity In single-slit diff…
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