| English | 意味 |
|---|---|
| gap/ɡæp/ | スリット |
| diffraction/dɪˈfrækʃn/ | 回折 |
| obstacle/ˈɒbstəkl/ | 障害物 |
| wavelength/ˈweɪvleŋθ/ | 波長 |
| ripple tank/ˈrɪpl tæŋk/ | 水波槽 |
| single slit/ˈsɪŋɡl slɪt/ | 単一スリット |
| diffraction grating/dɪˈfrækʃn ˈɡreɪtɪŋ/ | 回折格子 |
Heard but not seen
- You can hear someone around a corner — but you can't see them.
- Both sound and light reach the gap 缝, yet only sound bends around it.
- The difference is diffraction 衍射.
What diffraction is
- Diffraction is the spreading of a wave as it passes through a gap or around the edge of an obstacle 障碍物.
- All waves do it — water, sound, light, microwaves. The speed, wavelength and frequency do not change; only the direction spreads.
Waves adding and cancelling
Two overlapping waves add where they are in phase and cancel where out of phase — change the phase to see the result. This is what makes diffraction patterns.
Diffraction is the ____ of a wave as it passes through a gap.
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Diffraction is the spreading (bending) of a wave at a gap or obstacle.
All waves can diffract.
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Yes — water, sound, light and microwaves all spread at a gap or edge.
Diffraction is the ____ of a wave as it passes through a gap or around an obstacle.
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Spreading, not bending: refraction bends a wave at a boundary, and the two words are marked differently.
How much it spreads
- Gap much wider than $\lambda$ → the wave passes nearly straight through.
- Gap about the size of $\lambda$ → it fans out strongly.
Diffraction in a ripple tank 水波槽 — a wide gap (a) spreads the waves little, a narrow gap (b) much more
A wave spreads out the most when the gap is:
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When the gap ≈ the wavelength, the wave fans out strongly; a much wider gap lets it pass nearly straight.
Making the gap narrower makes the waves spread out ____.
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A narrower gap (closer to one wavelength) gives stronger diffraction.
Match each gap to how much the wave spreads out beyond it.
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Diffraction is greatest when the gap and the wavelength are about the same size, and fades as the gap gets much larger than the wavelength.
When does a wave diffract most through a gap? Select all that apply.
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This is why you hear round a doorway but cannot see round it: sound's wavelength is about a metre, light's is under a micrometre.
Why you hear but don't see
- Speech has $\lambda \approx 1\ \text{m}$ — close to a doorway's width, so it spreads round the corner.
- Light has $\lambda \approx 500\ \text{nm}$ — far smaller than the gap, so it barely spreads.
You can hear but not see around a corner because sound has a much larger wavelength than light.
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Sound's wavelength (~1 m) is near the gap size, so it diffracts; light's (~500 nm) is far smaller, so it barely does.
What diffracted light looks like
- Laser light through a single slit 单缝 gives a wide, bright central band with fainter bands either side.
- Through a diffraction grating 衍射光栅 (many slits) the light concentrates into sharp, narrow lines at definite angles: a tall central maximum, then symmetrical peaks at $\pm\theta_1$, $\pm\theta_2$ that get weaker further out.
- The angles obey $d\sin\theta = n\lambda$ — the next lesson but one uses it in full.
A grating has 500 lines per mm. What is the slit spacing d, in units of 1e-6 m?
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d = 1e-3/500 = 2.0e-6 m. Putting the lines per millimetre straight into d sin(theta) = n lambda is the standard error; you must invert it first.
Worked example: where the bright lines fall
Laser light of wavelength $600\ \text{nm}$ falls normally on a grating whose lines are $5.0 \times 10^{-6}\ \text{m}$ apart. Find the angle of the second-order line and describe the intensity graph from $-15^\circ$ to $+15^\circ$. A polarising filter is then placed in the beam.
- Second order: $\sin\theta = \dfrac{n\lambda}{d} = \dfrac{2 \times 600 \times 10^{-9}}{5.0 \times 10^{-6}} = 0.24$, so $\theta = 14^\circ$.
- First order: $\sin\theta = 0.12$, so $\theta = 6.9^\circ$.
- Graph: a tall narrow spike at $0^\circ$, smaller spikes at $\pm 6.9^\circ$, smaller again at $\pm 14^\circ$, and almost nothing in between.
- With the polarising filter: every spike is half as tall (unpolarised light through one filter), but the angles are unchanged — the filter does not alter the wavelength.
Light of wavelength $500\ \text{nm}$ falls normally on a grating with lines $4.0 \times 10^{-6}\ \text{m}$ apart. At what angle, in degrees, is the second-order maximum?
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$\sin\theta = \dfrac{n\lambda}{d} = \dfrac{2 \times 500 \times 10^{-9}}{4.0 \times 10^{-6}} = 0.25$, so $\theta = 14.5^\circ$.
Diffraction is not refraction and not reflection: the wave keeps the same speed, wavelength and frequency, and only its direction spreads. More spreading does not mean more energy — the same energy is shared over a wider region, so the wave beyond a narrow gap is weaker in any one direction.
A water wave passes through a narrow gap and spreads out. Which quantities stay the same? Select all that apply.
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Diffraction only changes the direction the energy travels in. Speed, wavelength and frequency are set by the medium and the source and do not change at a gap.
Seeing it in the lab
- Ripple tank: plane waves hit a barrier with a gap; narrow the gap (or lengthen $\lambda$ by slowing the paddle) and the curved wavefronts spread more.
- Laser and single slit: a pattern of bands on a distant screen; a narrower slit gives a wider central band.
- Laser and grating: a row of sharp dots; a finer grating (more lines per mm) pushes the dots further apart.
You've got it
- diffraction = a wave spreading through a gap or around an obstacle (all waves do it; speed, $\lambda$ and $f$ unchanged)
- most spreading when the gap is about one wavelength 波长 wide
- sound diffracts round corners (big $\lambda$); light hardly does (tiny $\lambda$), so it needs a slit or a grating to show it
- a grating gives sharp maxima at $d\sin\theta = n\lambda$; a polarising filter halves them without moving them