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.

Detector position $\text{—}$

Relative intensity $\text{—}$

First envelope minimum $\text{—}$

Order spacing $\text{—}$

Recorded slit count $\text{—}$

Total aperture span $\text{—}$

From the aperture to the Fourier plane

Change the opening to reshape the light

Single-slit envelopeDraws the ideal single-slit curve as a reference; the detector did not record it.Field-contribution guidesLines run from each opening through the lens to the chosen point in the focal plane. They sketch each opening's contribution to the field there; they are not traced rays.Wavelength

\lambda

550\,\mathrm{nm}

Slit width

a

60\,\mu\mathrm m

Slit pitch

d

180\,\mu\mathrm m

Number of slits

N

2

Lens focal length

f

300\,\mathrm{mm}

Uniform monochromatic light falls on identical rectangular slits, followed by an ideal Fourier lens. The detector sits one focal length behind the lens. The model uses scalar paraxial theory and leaves out aberrations, noise and averaging over a finite pixel. Each scan is normalized to its own on-axis intensity, so peak heights cannot be used to compare transmitted power. Transverse sizes are drawn enlarged.

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.

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 →MIT: interference and diffraction

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 misconceptionOnly rays touching the slit edges bend.

Better mental modelLight 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 misconceptionChanging slit spacing should equally change the single-slit envelope.

Better mental modelSlit 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

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.
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.
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.

Diffraction Studio

The aperture shape sets the pattern.

Diffraction: how apertures redistribute direction

Core mathematical model

Multi-slit intensity

Minima and principal maxima

Common difficulties

Diffraction is not edge reflection

Envelope and fringes come from different lengths

Run the experiment

Narrow one slit

Add a second slit

Add more slits

Related experiments and articles

Aperture, propagation, measurement