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Sandbox Physics

Waves · diffraction

Diffraction

On a 3D optical bench, an incident wave passes through one slit, two slits, or a grating and spreads onto a luminous screen. Colored fringes and a raised intensity profile rearrange as slit width, count, and wavelength change.

Interactive modelDiffraction
First minimum sin⁡θ\sin\theta0.000
Principal spacing Δ(sin⁡θ)\Delta(\sin\theta)— (single)
Slits1
First-order angle θ1\theta_1— (single)

Physics tutorial

Diffraction: how apertures redistribute direction

BackgroundAfter a wave passes through a finite aperture, every point across the opening acts like a secondary source. The distant pattern adds their phases in each direction.

Why it mattersDiffraction limits microscope and telescope resolution while allowing gratings to separate wavelengths.

Start with the essentials

Focus question
Why does a narrower slit make the transmitted wave spread more widely?
One-sentence intuition
Tighter spatial confinement broadens direction; more periodic apertures sharpen the allowed directions.

Core mathematical model

Multi-slit intensity

I(θ)=I0(sin⁡ββ)2(sin⁡Nαsin⁡α)2I(\theta)=I_0\left(\frac{\sin\beta}{\beta}\right)^2\left(\frac{\sin N\alpha}{\sin\alpha}\right)^2

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

Minima and principal maxima

asin⁡θ=mλ,dsin⁡θ=mλa\sin\theta=m\lambda,\qquad d\sin\theta=m\lambda

Slit width aa controls the envelope while spacing dd controls principal directions.

Common difficulties

Diffraction is not edge reflection

Typical misconceptionOnly rays touching the slit edges bend.

Better mental modelThe entire aperture contributes; the pattern comes from phase relations across a finite spatial range.

Envelope and fringes use different scales

Typical misconceptionChanging slit spacing should equally change the single-slit envelope.

Better mental modela sets the broad envelope; d and N set fringe positions and sharpness inside it.

Run the experiment

  1. 01

    Narrow one slit

    Choose Single slit and reduce a.

    What to observe: The central maximum widens and the first minimum moves outward.
  2. 02

    Add a second slit

    Switch to Double slit and vary d.

    What to observe: The envelope stays similar while internal spacing changes.
  3. 03

    Add more slits

    Choose Grating and raise N.

    What to observe: Principal positions remain while bright lines sharpen.