This unit shows how light behaves like a wave by spreading out through openings and by adding or canceling when two waves overlap. By the end, you should be able to predict where bright and dark fringes land and use measured fringe positions to calculate a wavelength.
Read the overview first, then work through each topic's notes and try the checkpoint question before checking the answer.
In earlier units you treated light mostly as rays that travel in straight lines. This unit shows where that picture breaks down. When openings get small or waves overlap, light produces patterns that only make sense if it's a wave.
Honors Physics Unit 17 covers diffraction and interference of waves, mostly light. You'll use Huygens's principle to explain why waves spread through openings. You'll use superposition and path difference to explain bright and dark fringes, and you'll apply and its small-angle form to double slits and diffraction gratings. The unit finishes with applications, including thin-film colors, anti-reflective coatings, lasers and coherence, spectroscopy, and the resolution limits of telescopes and microscopes.
Huygens's principle treats every point on a wavefront as a source of new wavelets, so an opening acts like a new source that sends waves out at many angles. Sound, with wavelengths around a meter, bends around doorways easily. Visible light, around 400-700 nm, only spreads noticeably through very narrow slits.
For waves that start in phase and travel through the same medium, a path difference of gives constructive interference. A path difference of gives destructive interference. The waves cancel completely only if their amplitudes are equal.
Visible light's wavelength is a few hundred nanometers, but fringes can be separated by millimeters on a screen. With a known slit spacing, you can measure the screen distance and a fringe position to calculate . Gratings use the same idea to separate light into spectra that identify elements.
Double slits, gratings, thin films, and single slits all involve overlapping waves. Their phase difference determines whether they reinforce or cancel. To predict a pattern, account for path differences and for any phase changes caused by reflection.
Light acts like a wave, so it spreads out after passing through an opening (diffraction), and overlapping waves combine (interference).
A diffraction grating works like a double slit with hundreds or thousands of slits.
Light acts like a wave, so it spreads out after passing through an opening (diffraction), and overlapping waves combine (interference). Superposition is the rule underneath both. At any point, the total displacement equals the sum of the individual waves' displacements.
Huygens's principle explains the spreading. Every point on a wavefront acts as a source of small wavelets, and the new wavefront is the envelope of those wavelets. Diffraction is strongest when the opening is about the size of the wavelength or smaller.
For two waves that start in phase and travel through the same medium, the path difference is the extra distance one travels compared with the other. A path difference of gives constructive interference, while gives destructive interference. Complete cancellation at a dark fringe requires equal amplitudes.
For two slits separated by , bright fringes satisfy . When the screen distance is much bigger than the fringe distance , this becomes , or . The central bright fringe is .
Worked example. Slits 0.20 mm apart sit 1.5 m from a screen. The second bright fringe () is 9.0 mm from the center. Convert to meters first, then substitute: m. That's 600 nm, orange light, which is a reasonable visible wavelength.
If you move the slits closer together while keeping the wavelength and screen distance the same, do the fringes spread out or bunch together? (Answer: They spread out. Since , a smaller makes each fringe distance larger.)
| Feature | Single slit | Double slit |
|---|---|---|
| Main equation | $a\sin\theta = m\lambda$ with m = 1, 2, 3, ... | $d\sin\theta = m\lambda$ with m = 0, 1, 2, ... |
| What the equation locates | Dark fringes | Bright fringes |
| Central bright fringe | About twice as wide as the side fringes | About the same width as other fringes at small angles |
| What is interfering | Wavelets from different parts of one slit | Waves coming from two separate slits |
A diffraction grating works like a double slit with hundreds or thousands of slits. It uses the same equation, , where is the spacing between neighboring lines. More slits make each bright maximum much sharper, so gratings split light into clean spectra. Longer wavelengths bend to larger angles, so red lands farther out than violet. Spectroscopes use this to identify elements from their spectral lines.
Worked example. A grating has 600 lines/mm, so mm m. For 500 nm light in first order, , so . Since can't exceed 1, the highest order is , so you'll see orders up to .
Thin-film interference comes from light reflecting off both the top and bottom of a film, like a soap bubble or oil slick. The phase difference depends on the film's thickness and refractive index, the angle of the light, and any phase changes on reflection. Anti-reflective coatings use destructive interference to reduce reflection, often for a chosen wavelength and angle.
Stable interference fringes need sufficient coherence, meaning the relevant waves maintain a predictable phase relationship. Laser light is often used for fringes and holograms, but spectroscopy and diffraction-limited imaging do not require a laser. Diffraction also limits resolution. A circular opening of diameter can just separate two points at , so bigger telescopes see finer detail.
If you swap to a grating with 1200 lines/mm, what is the first-order angle for 500 nm light? (Answer: m, so and . More lines per mm spreads the spectrum to wider angles.)
| Term | Definition |
|---|---|
| Diffraction | The spreading or bending of a wave as it passes through an opening or around an obstacle. |
| Interference | The combining of two or more overlapping waves into a new wave pattern by adding their displacements. |
| Superposition principle | When waves overlap, the total displacement at any point is the sum of the individual waves' displacements. |
| Constructive interference | The addition of waves in phase, crest on crest. For waves that start in phase and travel through the same medium, this occurs when their path difference is a whole number of wavelengths. |
| Destructive interference | The addition of waves that are half a cycle out of phase, crest on trough. For waves that start in phase and travel through the same medium, this occurs when their path difference is a half-integer number of wavelengths. Equal amplitudes are needed for complete cancellation. |
| Fringe | One of the bright or dark bands that appear on a screen in a diffraction or interference pattern. |
| Young's double-slit experiment | An experiment where light passes through two narrow slits and forms interference fringes, showing that light behaves as a wave. The fringes are approximately evenly spaced on a flat screen at small angles. |
| Coherent sources | Wave sources with the same frequency and a constant phase difference, such as a laser split by two slits. |
| Resolution | The smallest angular separation at which an optical instrument can still distinguish two separate objects, limited by diffraction through its opening. |
Counting starts at zero for bright fringes, so the central maximum is m = 0 and the first bright fringe on either side is m = 1. If a problem says the third bright fringe from the center, use m = 3, and measure x from the middle of the central fringe.
The equations look the same, but for a single slit gives dark fringes, while for double slits and gratings gives bright ones. Check which setup you have before deciding what the equation is locating.
Slit spacings come in mm, screen distances in m, and wavelengths in nm, so plugging in raw numbers gives answers off by factors of 1000 or more. Convert everything to meters first, then convert your final wavelength to nm and check that it lands between about 400 and 700 nm for visible light.
It's the reverse. Spreading is strongest when the opening is close to the wavelength, so narrowing a slit makes the pattern wider. A wide window lets light through almost straight, which is why you don't see diffraction from everyday doorways with light.