---
title: "Light after a Narrow Slit Interactive Lab | Sandbox Physics"
description: "Why does a narrower opening spread light farther?"
canonical_url: "https://sandboxphysics.com/labs/diffraction/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/diffraction/"
last_modified: "2026-10-27"
---

Optics · aperture · Fourier plane

# Diffraction Studio

**Why does a narrower opening spread light farther?** Squeezing a wave into a narrower space widens the range of directions it travels in, so a narrower slit gives a wider diffraction envelope. Adding more evenly spaced slits does something different: it sharpens the allowed directions into narrow orders.

Change the width, spacing and number of slits on an optical bench. Record the pattern in the focal plane, look at the single-slit envelope, and find where whole diffraction orders disappear.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

The lit aperture, an ideal lens and the detector in the focal plane are computed as one model. Nanometres, micrometres and millimetres are converted explicitly, and the drawing is enlarged so the features are visible.

Read the wave field

## The aperture shape sets the pattern.

Move the probe $0.000\,\mathrm{mm}$

Mint: current record. Coral: saved record. Gold: single-slit envelope. The cursor selects an acquired sample; all numbers and CSV values stay linear. Screen brightness uses a square-root display mapping, clipped at one, to reveal faint fringes.

$$
\frac{I(x)}{I(0)}=\operatorname{sinc}^2\!\left(\frac{\pi a x}{\lambda f}\right)\left|\frac1N\sum_{n=0}^{N-1}e^{-2\pi i(n-(N-1)/2)dx/(\lambda f)}\right|^2
$$

The pattern is a deterministic ideal line scan, not photon counts or a reconstruction. The chart covers only the central horizontal slice of long rectangular slits. The optical layout is schematic and transverse scales differ from the propagation scale.

[Return to two sources →](https://sandboxphysics.com/labs/wave-interference/) [MIT: interference and diffraction](https://ocw.mit.edu/courses/6-007-electromagnetic-energy-from-motors-to-lasers-spring-2011/resources/mit6_007s11_lec27/)

Physics tutorial

## Diffraction: how apertures redistribute direction

**Background** After a wave passes through a finite aperture, every point across the opening acts like a secondary source. The back focal plane of an ideal lens records their Fourier superposition.

**Why it matters** Diffraction limits the resolution of microscopes and telescopes, and it also lets gratings separate wavelengths.

Start with the essentials

- **Focus question**: Why does a narrower slit make the transmitted wave spread more widely?
- **One-sentence intuition**: The narrower the opening, the wider the spread of directions; the more periodic openings there are, the sharper the allowed directions.

### Core mathematical model

#### Multi-slit intensity

$$
\frac{I(x)}{I(0)}=\operatorname{sinc}^2\beta\left(\frac{\sin N\alpha}{N\sin\alpha}\right)^2,\quad\beta=\frac{\pi ax}{\lambda f},\quad\alpha=\frac{\pi dx}{\lambda f}
$$

The first factor is the single-slit envelope; the second is fine structure from $N$ slits.

#### Minima and principal maxima

$$
x_{\min}=\frac{m\lambda f}{a}\;(m\ne0),\qquad x_{\mathrm{order}}=\frac{m\lambda f}{d}
$$

Slit width $a$ sets the envelope, and slit spacing $d$ sets the directions of the principal maxima.

### Common difficulties

#### Diffraction is not edge reflection

**Typical misconception** Only rays touching the slit edges bend.

**Better mental model** Light from the whole aperture contributes, and the pattern comes from the phase differences across its finite width.

#### Envelope and fringes come from different lengths

**Typical misconception** Changing slit spacing should equally change the single-slit envelope.

**Better mental model** Slit width sets the broad envelope; slit spacing and slit count set where the fringes inside it fall and how sharp they are.

### Run the experiment

1. 01

   #### Narrow one slit

   Choose Single slit, keep the scan, reduce the width and record again.

   **What to observe:** The central maximum widens and the first minimum moves outward.

2. 02

   #### Add a second slit

   Switch to Double slit, vary the pitch and record again.

   **What to observe:** The envelope stays about the same, but the fringe spacing inside it changes.

3. 03

   #### Add more slits

   Choose Eight slits, then try Missing orders.

   **What to observe:** More slits make the principal maxima sharper. In the Missing orders preset, every second nonzero order lands on a zero of the envelope and disappears.

Physical conclusion

The size of the opening sets how widely light spreads; the period and the number of openings set which directions it goes and how sharply.

## Related experiments and articles

Continue exploring

### Aperture, propagation, measurement

Change one physical assumption at a time: slit count, coherence, aperture shape or propagation distance.

1. [You are here **Diffraction Studio** Start with a focal-plane scan of one, two or many slits.](https://sandboxphysics.com/labs/diffraction/)
2. [Lab **Young Double-Slit Bench** Add unequal amplitudes and partial coherence to two slits.](https://sandboxphysics.com/labs/young-double-slit-bench/)
3. [Lab **Aperture Diffraction Studio** Draw a two-dimensional opening and inspect its complement.](https://sandboxphysics.com/labs/aperture-diffraction-studio/)
4. [Lab **Huygens–Fresnel Propagation Lab** Move the receiving plane from near field toward far field.](https://sandboxphysics.com/labs/huygens-fresnel-propagation-lab/)
5. [Lab **Diffraction-Grating Spectrometer** Connect groove spacing and illuminated count to spectral resolution.](https://sandboxphysics.com/labs/diffraction-grating-spectrometer/)

Waves & optics · Starter path

## From one ray to interference measurement

Start with refraction, find where the ray picture stops working, then use interference to measure tiny distances.

[Start here → **Optical Boundary Explorer** Turn the incident angle and watch reflected and transmitted power trade off. Then switch to the critical-angle scene. Observe · 11 min](https://sandboxphysics.com/labs/optical-boundary-explorer/)

1. [1 Optical Boundary Explorer](https://sandboxphysics.com/labs/optical-boundary-explorer/)
2. [2 Rainbow Caustic Observatory](https://sandboxphysics.com/labs/rainbow-laboratory/)
3. [3 Camera Obscura](https://sandboxphysics.com/labs/camera-obscura/)
4. [4 Coherent Wave Composer](https://sandboxphysics.com/labs/coherent-wave-composer/)
5. [5 Young Double-Slit Bench](https://sandboxphysics.com/labs/young-double-slit-bench/)
6. [6 Michelson Precision Lab](https://sandboxphysics.com/labs/michelson-precision-lab/)

[View the full path →](https://sandboxphysics.com/topics/waves-and-optics/#starter-path)