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Đã giới thiệu| English | Ý nghĩa |
|---|---|
| coherent/kəʊˈhɪərənt/ | Having a fixed phase relationship over time. |
| path difference/pæθ ˈdɪfrəns/ | The difference in distance travelled by two waves to the same point. |
| diffraction/dɪˈfrækʃn/ | Nhiễu xạ |
Two bright waves, darkness
- Two equal coherent 相干的 beams, each of intensity $I_0$, meet. Depending on their phase difference the result is anywhere from $4I_0$ to $0$.
- GRE optics tests superposition, path and phase, double- and single-slit patterns, and when wave effects matter.
Add amplitudes, then square
- Intensity $\propto$ amplitude$^2$. Two equal waves with phase difference $\varphi$: $I = 2I_0(1 + \cos\varphi)$.
- In phase: amplitude $2A$, intensity $4I_0$. Out of phase ($\varphi = \pi$): zero. Adding intensities would always give $2I_0$ — only true for incoherent light.
Two equal coherent waves (each $I_0$) meet with $\varphi = \pi/2$. Intensity in units of $I_0$?
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Two equal waves give $I = 2I_0(1 + \cos\varphi)$. With $\varphi = \pi/2$, $\cos\varphi = 0$, so $I = 2I_0$: the intensities simply add.
For coherent waves, the total intensity includes an interference term that depends on the phase difference.
Độ khó 1/5 · 100 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
True. Amplitudes add, so I = I₁ + I₂ + 2√(I₁I₂) cos φ; only for incoherent waves do the intensities simply add.
Path difference 程差 and the double slit
- $\varphi = 2\pi\Delta/\lambda$. Coherent sources keep a stable phase relation.
- Double slit: bright fringes at $d\sin\theta = m\lambda$; spacing on a distant screen $\Delta y = \lambda L/d$.
$\lambda = 600$ nm, $d = 0.30$ mm, $L = 2.0$ m: $\Delta y = \dfrac{600\times10^{-9} \times 2}{3\times10^{-4}} = 4$ mm.
Bright or dark?
Use path difference to predict interference.
λ = 500 nm, slit separation 0.25 mm, screen 1.5 m away. Fringe spacing in mm?
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$500\times10^{-9} \times 1.5 / 2.5\times10^{-4}$ m.
A path difference of $\lambda/4$ gives a phase difference of
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A whole wavelength of path is $2\pi$ of phase, so a quarter wavelength is $2\pi/4 = \pi/2$.
Single-slit diffraction 衍射
- Minima at $a\sin\theta = m\lambda$, $m = \pm1, \pm2, \dots$ — not $m = 0$, which is the central maximum.
- Central maximum width on a screen: $2\lambda L/a$. A narrower slit spreads the light more.
The central maximum is not $m = 0$ in the minima condition: $a\sin\theta = 0$ is the brightest point, not a dark one.
A 0.10 mm slit, λ = 500 nm, screen 1.0 m away. Width of the central maximum in mm?
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$2\lambda L/a = 2 \times 5$ mm.
Rays or waves?
- Geometric optics works when apertures are much larger than $\lambda$; diffraction dominates when they are comparable.
- Thin lens: $\frac1f = \frac1{d_o} + \frac1{d_i}$ with a stated sign convention (real image: $d_i > 0$).
Recap
- Coherent waves: add amplitudes, then square.
- $\varphi = 2\pi\Delta/\lambda$; double-slit maxima $d\sin\theta = m\lambda$.
- Single-slit minima $a\sin\theta = m\lambda$ with $m \neq 0$.
- coherent: Having a fixed phase relationship over time.
- path difference: The difference in distance travelled by two waves to the same point.