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Interference and Young's double slit
Overlap two sets of waves and there are places where they cancel: light plus light making darkness. Young's double slit turns that idea into evenly spaced fringes you can measure with a ruler, and the spacing hands you the wavelength of light.
Builds on Diffraction and the single slit.
IN THIS TOPIC
- Predict constructive or destructive interference from a path difference.
- Explain what coherence means and why it is needed for a stable pattern.
- Use w = λD / s on the double-slit experiment, and describe the white-light pattern.
WHAT YOU PROBABLY THINK
Shine two lights on the same spot and you simply get a brighter spot.
Superposition and path difference
When two waves occupy the same place, their displacements add. Two crests arriving together make a larger crest, constructive interference; a crest arriving with a trough makes cancellation, destructive interference. Whether a given point gets reinforcement or cancellation depends on the path difference, how much further that point sits from one source than from the other.
A whole number of wavelengths of path difference delivers the two waves in phase; an extra half wavelength delivers them in antiphase. For the dark places to stay dark, the sources must be coherent: the same frequency, with a constant phase difference between them. Two separate lamps emit light in random, unrelated bursts, so their pattern reshuffles billions of times a second and the eye sees a uniform glow. A laser is the convenient source because its light is coherent and effectively monochromatic; the classic alternative is one lamp behind a single slit, split into two.
Young's double slit
Illuminate two narrow slits, a distance s apart, with coherent light and view a screen a distance D away. Each slit diffracts, the two spreading waves overlap, and the screen shows fringes: bright bands where the path difference is nλ, dark bands between them.
The fringe spacing w, centre of one bright fringe to the centre of the next, comes from the geometry:
The equation says what the pattern looks like. Because w is the same between every pair of neighbours, the fringes are evenly spaced, and in the AQA treatment they are equally bright. It also says how to change them: a longer wavelength, a more distant screen or closer slits all widen the spacing. Visible-light wavelengths are a few hundred nanometres, so with millimetre slit separations the experiment needs D of a metre or more to make w visible.
WORKED EXAMPLE
A laser of wavelength 650 nm illuminates two slits 0.50 mm apart, and fringes form on a screen 3.0 m away. Find the fringe spacing.
Convert to metres first: λ = 650 × 10− 9 m and s = 0.50 × 10− 3 m.
w = λD / s = (650 × 10− 9 × 3.0) / (0.50 × 10− 3) = 3.9 × 10− 3 m, a fringe spacing of 3.9 mm: comfortably visible, and measurable with a ruler.
White light, and a word on safety
Replace the laser with white light and every wavelength draws its own set of fringes with its own spacing. The central fringe, where the path difference is zero for every colour, stays white. The fringes either side are spectra, with blue on the inner edge of each, because the shorter wavelength has the smaller spacing, and red on the outer edge. A few fringes out, the overlapping colours merge and the pattern fades.
Lasers make the experiment easy and also make it the one place in the optics lab where care is compulsory. Never look into the beam or point it at anyone, keep it away from reflective surfaces, and stand behind the laser while it is on. Even a classroom laser can damage the retina faster than the blink reflex can respond.
THE EXAM BIT
- Coherent means constant phase difference and the same frequency. The word “constant” carries the mark; “in phase” is a different, stronger claim and is wrong as a definition.
- Fringe questions live or die on unit conversion: nm and mm into metres before substituting into w = λD/s.
- Know each symbol's place: w and s are the two small lengths (fringe spacing, slit separation), D the large one. Swapping w and s is the classic error, and the sanity check is that w should come out around millimetres.
- Double-slit fringes are evenly spaced and equally bright. Keep that phrase distinct from the single-slit pattern, whose central maximum is wider and brighter.
- If asked for a safety precaution with lasers, give a specific one: do not look along the beam, or remove reflective objects from the bench. “Be careful” earns nothing.
CHECK YOURSELF
In a double-slit experiment, light of wavelength 630 nm falls on slits 0.45 mm apart, and the screen is 2.0 m away. Calculate the fringe spacing.
Show a hint
Put every length into metres before you substitute.
Show the answer
λ = 630 × 10− 9 m, s = 0.45 × 10− 3 m, D = 2.0 m.
w = λD / s = (630 × 10− 9 × 2.0) / (0.45 × 10− 3) = 2.8 × 10− 3 m, so the bright fringes sit 2.8 mm apart.
Bright: paths differ by nλ.
Dark: paths differ by (n + ½)λ.
No animated video for this topic yet; these notes stand alone. InkPhysics on YouTube.