Double-Slit Interference and Diffraction Gratings
Introduced| English | Meaning |
|---|---|
| diffraction grating/dɪˈfrækʃn ˈɡreɪtɪŋ/ | An optical component with many equally spaced slits or grooves that produces interference maxima at particular angles. |
Shine light through two slits — and get stripes, not two lines
- Send light through two narrow slits and the screen shows a row of bright and dark stripes.
- Not two bright lines as you'd expect — an interference pattern.
- This is Young's double-slit experiment, and it proved light is a wave.
- The same idea, with thousands of slits, becomes a diffraction grating.
How the fringes form
- Light spreads (diffracts) from each slit, and the two sets of waves overlap and interfere.
- Where they arrive in phase, they add — a bright fringe.
- Where they arrive out of phase, they cancel — a dark fringe.
- The pattern is a direct picture of constructive and destructive interference.
Two waves interfering
Change the phase difference and watch two waves add to bright (in phase) or cancel to dark (out of phase).
The double-slit interference pattern is evidence that light is a:
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Interference is a wave phenomenon, so the fringes prove light is a wave.
The bright-fringe condition
- Bright fringes appear where the path difference from the two slits is a whole number of wavelengths.
- The condition is $d\sin\theta = m\lambda$, with $m = 0, 1, 2, \ldots$
- Closer slits (smaller $d$) or a longer wavelength spread the fringes further apart.
- Measuring the fringe spacing lets you calculate the wavelength of the light.
A bright fringe forms where the path difference from the two slits is:
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Bright fringes need $d\sin\theta = m\lambda$ — a whole number of wavelengths.
If the slit separation $d$ is halved, the fringe spacing:
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Fringe spacing goes as $1/d$, so halving $d$ doubles the spacing.
A dark fringe forms where waves from the two slits arrive in phase.
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False. In-phase arrival gives constructive interference, a bright fringe. Dark fringes form where the waves arrive out of phase and cancel.
Diffraction gratings
- A diffraction grating 衍射光栅 has thousands of fine slits packed together.
- It splits light into very sharp, bright spots — far cleaner than two slits.
- It also spreads different colours by different angles, making a spectrum.
- Gratings are used in spectrometers to identify the elements in stars and samples.
A device with thousands of fine slits that splits light into sharp spots is a diffraction ____.
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A diffraction grating gives very sharp, bright maxima.
Select all true statements about the double slit and gratings.
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Bright = whole-wavelength path difference; interference proves light is a wave; gratings make spectra. The pattern is interference, not independent torches.
The double-slit fringes come from interference, not from the slits acting as tiny torches — that's why you get a pattern of stripes, not two bright bars. Bright fringes need a path difference of a whole number of wavelengths ($d\sin\theta = m\lambda$); half-wavelengths give dark fringes.
In a double-slit setup, the slit separation is halved. What happens to the fringe spacing?
- Fringe spacing goes as $1/d$, so halving $d$ doubles the spacing.
- The bright stripes move further apart on the screen.
Young's double slit makes bright and dark fringes by interference — bright where $d\sin\theta = m\lambda$ (whole-number path difference). Closer slits or longer wavelengths spread the fringes wider. A diffraction grating (thousands of slits) gives sharp spots and splits light into a spectrum.
Write from a path difference of 1200 nm
- Light of wavelength 600 nm passes through two slits.
- The second bright fringe from the centre needs a path difference of two wavelengths. Find that path difference.
Light of wavelength 600 nm falls on a double slit. For the second bright fringe out from the centre, the path difference is two wavelengths. What is that path difference, in nanometres?
Two wavelengths of 600 nm make 1200 nm.
What is the path difference at that second bright fringe?
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The second bright fringe needs two wavelengths.