--- title: "Intensity in Single-Slit and Double-Slit Diffraction" description: "Adding the contributions from every point across a slit gives the intensity as a function of angle, not only the positions of the minima. A real two-slit pattern is that single-slit envelope multiplie" canonical: https://lightmysky.com/learn/science/intensity-in-single-slit-and-double-slit-diffraction-mt_HURhzZdIkM source: https://lightmysky.com/learn/science/intensity-in-single-slit-and-double-slit-diffraction-mt_HURhzZdIkM.md retrieved: 2026-09-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Intensity in Single-Slit and Double-Slit Diffraction Adding the contributions from every point across a slit gives the intensity as a function of angle, not only the positions of the minima. A real two-slit pattern is that single-slit envelope multiplied by the two-slit fringes. Subject: Science · Area: Waves, Light & Sound · Ages 20 to 21 Page: https://lightmysky.com/learn/science/intensity-in-single-slit-and-double-slit-diffraction-mt_HURhzZdIkM ## Ready when they can - Derives the single-slit intensity pattern by adding contributions across the slit - Explains missing orders in a two-slit pattern using the diffraction envelope - Predicts how the pattern changes when the slit is widened ## Lesson: What sets the brightness across a slit pattern Picture the slit as a row of tiny sources side by side. Each sends a wavelet, and at any screen angle their crests arrive with shifted phases. Add them as phasors head to tail: a straight line at center, a curling spiral off center. The curl is summed up in beta, pi times slit width times sine of angle over wavelength, and the brightness is the central brightness times sine of beta over beta, squared. The spiral closes into full circles wherever beta is a whole multiple of pi, which is exactly where slit width times sine of angle equals a whole number of wavelengths. Those dark angles fence in a bright central peak about two wavelengths over slit width wide. Widen the slit and the peak narrows: with 550 nm light and a 2.00 micrometer slit the first dark angles sit at 16.0 and 33.4 degrees. **Example.** With two slits the interference fringes, separation times sine equals order times wavelength, get dimmed by the single-slit envelope. Where a bright fringe lands on an envelope dark spot, that order goes missing: with width twice and separation six times the wavelength, orders plus and minus 3 vanish, and the same repeats at multiples. With 0.020 mm slits 0.20 mm apart in 500 nm light, orders plus and minus 10 vanish, and again at 20, leaving 19 bright fringes in the central peak. **Tip.** Nearly all the light sits in the central peak: off center the phasors curl almost one and a half turns, so the leftover sum is short and the first side bump reaches only about 0.045 of the center. When you work both equations at once, give the two whole numbers different letters so orders and minima never mix. **Recap.** Wavelets across each slit sum to an envelope that dims the two-slit fringes and deletes whole orders. ## Practice 8 questions on this page, each with its working shown. ## Needs first - [Phasor Addition and the Mathematics of Interference](https://lightmysky.com/learn/science/phasor-addition-and-the-mathematics-of-interference-mt_dxh7HHbIUw) - [Single-Slit Diffraction and the Limit of Resolution](https://lightmysky.com/learn/science/single-slit-diffraction-and-the-limit-of-resolution-mt_qiG0fGadBU) - [The Diffraction Grating and Measuring Wavelength](https://lightmysky.com/learn/science/the-diffraction-grating-and-measuring-wavelength-mt_yIjB-uJuFt) ## Opens up - [X-Ray Diffraction and the Bragg Condition](https://lightmysky.com/learn/science/x-ray-diffraction-and-the-bragg-condition-mt_qEDplGeIkB)