---
title: "Young Double-Slit Bench Interactive Lab | Sandbox Physics"
description: "How do slit width, slit spacing, phase and coherence each change a double-slit pattern?"
canonical_url: "https://sandboxphysics.com/labs/young-double-slit-bench/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/young-double-slit-bench/"
last_modified: "2026-10-27"
---

Optics 042 · Interference, coherence, cavities, and metrology

# Young Double-Slit Bench

**How do slit width, slit spacing, phase and coherence each change a double-slit pattern?** The slit separation fixes the fringe spacing: the farther apart the slits, the closer the fringes. Each slit's width sets the broad diffraction envelope, and a fringe that falls on one of its zeros goes missing. A phase shift slides the fringes under that envelope, and partial coherence lowers their contrast.

Separate diffraction from interference on a 3D double-slit bench, then measure missing orders, the effect of partial coherence and the contrast when the two amplitudes differ.

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

The pattern is the scalar paraxial far field. The coherence between the slits is constant, each axis is magnified independently, and intensity is referenced to the current geometry.

Physics tutorial

## Audit the physics of Young Double-Slit Bench

**Background** A slit of finite width sends light out over a spread of angles, not as one narrow ray. In the scalar paraxial far field, the screen sees the Fourier transform of the aperture: $U(y)\propto\int t(s)e^{-i2\pi ys/(\lambda L)}\,ds$. Light across each slit is coherent, and each slit is infinitely tall. Because the two slits have equal widths, they share one sinc amplitude. The two highlighted lines in the 3D view show phase paths to the probe; they are not a solved near-field intensity, and light does not travel only along them. The openings really change width and centre separation, and the screen really moves.

**Why it matters** How do slit width, slit spacing, phase and coherence each change a double-slit pattern?

Start with the essentials

- **Focus question**: How do slit width, slit spacing, phase and coherence each change a double-slit pattern?
- **One-sentence intuition**: Two independent length scales shape the pattern on the screen: $\Delta y=\frac{\lambda L}{d},\qquad y_1=\frac{\lambda L}{a}$. The slit width sets the gold diffraction envelope, and the slit separation sets the cyan interference period. Because the pattern is their product, an order can go missing even where the two waves are in phase. Changing the phase moves the fringes but not the envelope.

### Core mathematical model

#### Two Fourier amplitudes

$$
\begin{aligned}u_-&=\operatorname{sinc}(\beta)e^{i\alpha},\quad u_+=r\operatorname{sinc}(\beta)e^{i(\phi-\alpha)}\\\beta&=\frac{\pi ay}{\lambda L},\quad\alpha=\frac{\pi dy}{\lambda L},\quad\operatorname{sinc}(x)=\frac{\sin x}{x},\quad\operatorname{sinc}(0)=1\end{aligned}
$$

The left slit is centred at a negative position and the right slit at a positive one. The sign convention of the Fourier transform fixes which way a positive phase shifts the fringes. The sinc factor changes sign at each zero. Both slit amplitudes carry that same sign, so it has to stay in their phasors.

#### Mutual coherence weights only the cross term

$$
\frac{I}{I_{\mathrm{ref}}}=\frac{|u_-|^2+|u_+|^2+2\mu\operatorname{Re}(u_-^*u_+)}4=\mu\frac{|u_-+u_+|^2}4+(1-\mu)\frac{|u_-|^2+|u_+|^2}4
$$

Lowering the coherence weakens only the cross term. The panel shows the coherent part and the incoherent part separately; partial coherence is not represented by one made-up field. The mutual coherence at the two slits is set to a constant real value. The SPEAR3 paper motivates the contrast measurement, but its source-size inversion and optical train are not simulated here.

#### Missing orders and phase-scan contrast

$$
y_m=\left(m+\frac{\phi}{2\pi}\right)\frac{\lambda L}{d},\quad y_n=n\frac{\lambda L}{a},\quad V_{\mathrm{phase}}=\frac{2\mu r}{1+r^2}
$$

An order where the two waves are in phase disappears if it lands on an envelope zero away from the centre. With zero phase and a separation three times the width, every third order is missing. The alignment ticks are not the exact local maxima of the full product. Visibility is measured by scanning the phase at a fixed point where the envelope is not zero; unequal amplitudes lower it even at full coherence. At an envelope zero the local contrast is undefined.

#### Reference scale and where the approximation holds

$$
\frac{I_{\mathrm{ref}}}{I_{\mathrm{inc}}}=\frac{4a^2}{\lambda L},\quad F_A=\frac{[(d+a)/2]^2}{\lambda L}\le0.081,\quad\frac{|y|}{L}\le0.020
$$

For infinitely tall slits, the one-dimensional Fresnel kernel gives this reference for the current geometry, relative to the incident intensity. It falls off as one over the distance, not as the inverse square that a finite two-dimensional aperture gives in the far field. Every plot runs from zero to one on this reference scale and is never rescaled to its current maximum. The far-field check uses the whole horizontal half-aperture, not just one slit width. Screen colours are illustrative RGB, not calibrated colorimetry. The model is an approximation; it is not a Maxwell solver, a Fresnel near-field calculation, a finite-height slit model or a photon-counting simulation.

### Common difficulties

#### Wider slits do not widen the envelope

**Typical misconception** Changing slit width and separation should have the same effect because both make the aperture bigger.

**Better mental model** They enter as different Fourier factors. Widening each opening narrows the envelope; moving the centres apart packs the fringes closer together. Changing the phase shifts the alignment ticks. Lowering the coherence fills in the dark gaps between fringes but leaves the envelope zeros in place. With the right amplitude at zero, a single-slit envelope remains, at one quarter of the equal-slit reference.

### Run the experiment

1. 01

   #### Scene 1: Narrow-slit interference

   In the narrow-slit preset, vary the centre separation, then the screen distance and the wavelength. Shift-drag the cursor, or use its slider, to put it on a dark fringe. Set the phase to 180 degrees and the centre turns dark.

   **What to observe:** Changing the separation changes the fringe period but not the envelope; distance and wavelength stretch both. The apparatus, the amplitudes, the profile and the readout all use the same white probe.

2. 02

   #### Scene 2: Every third order missing

   Choose the missing-order preset. Measure the third phase-alignment tick where it sits on the gold envelope zero, then change the slit width or the phase so the two no longer coincide.

   **What to observe:** The third order is dark because the amplitude from each finite slit vanishes there; the two slits have not suddenly lost coherence. The initial phase does not move the envelope zero.

3. 03

   #### Scene 3: Partial coherence, not dimming

   Choose partial coherence. Reduce the coherence to zero; then restore it and lower the right amplitude to zero instead. Compare the cross-term contribution with the baseline.

   **What to observe:** With zero coherence, the screen shows just the sum of the two separate intensities. Blocking one slit removes the interference completely. Unequal amplitudes and partial coherence lower the contrast for different reasons.

Physical conclusion

To understand a Young experiment, follow the chain from the real slit openings to the complex aperture amplitudes, their statistical cross term, the detector pattern on a fixed reference scale and the far-field limits. Glowing lines in a picture cannot show any of these links on their own.

## 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. [Lab **Diffraction Studio** Start with a focal-plane scan of one, two or many slits.](https://sandboxphysics.com/labs/diffraction/)
2. [You are here **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/)

Starter path · Step 5 of 6

## From one ray to interference measurement

[Next step → **Michelson Precision Lab** Move one mirror by less than a micrometre and follow the fringes as they pass. Interference becomes a ruler. Transfer · 13 min](https://sandboxphysics.com/labs/michelson-precision-lab/)

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)