Single-slit diffraction occurs when light passes through a narrow opening whose width is comparable to the wavelength. Instead of forming a sharp geometric shadow, the wave spreads out and produces a bright central maximum with weaker side maxima and dark minima.
The standard explanation uses the idea that different points across the slit act like sources of secondary waves. At some angles, these contributions cancel each other. For a slit of width \(a\), destructive interference occurs when
\[
a\sin\theta_m = m\lambda,\qquad m=\pm1,\pm2,\dots
\]
These are the angles of the diffraction minima.
For small angles, which is the usual classroom approximation,
\[
\sin\theta \approx \theta,
\]
so the minima angles become
\[
\theta_m \approx \frac{m\lambda}{a}.
\]
The first minimum is therefore at
\[
\theta_1 \approx \frac{\lambda}{a}.
\]
Since the central bright maximum lies between the first minima on both sides, its angular width is approximately
\[
2\theta_1 \approx \frac{2\lambda}{a}.
\]
The full intensity distribution is described by
\[
I = I_0\,\operatorname{sinc}^2(\beta),
\]
where
\[
\beta = \frac{\pi a\sin\theta}{\lambda}
\]
and
\[
\operatorname{sinc}(\beta)=\frac{\sin\beta}{\beta}.
\]
This function gives a large central peak and progressively weaker side lobes. The zeros of the sinc function match the minima condition above.
The formulas show the main trends clearly. If the wavelength increases, the diffraction pattern spreads out more. If the slit becomes narrower, the diffraction pattern also spreads out more. This is the opposite of what students often expect from simple ray diagrams, and it is one of the important signatures of wave behavior.
Using the sample values \(\lambda=600\text{ nm}\) and \(a=0.2\text{ mm}\),
\[
\theta_1 \approx \frac{600\times10^{-9}}{0.2\times10^{-3}}
= 3.0\times10^{-3}\text{ rad}.
\]
So the first minimum is at about
\[
\theta_1 \approx 0.003\text{ rad},
\]
which matches the expected classroom result. The central maximum width is then approximately
\[
2\theta_1 \approx 0.006\text{ rad}.
\]
Single-slit diffraction is closely related to many real optical systems. Apertures in cameras, microscopes, and telescopes all produce diffraction effects. At more advanced level, the topic extends to circular apertures, Airy disks, and resolution criteria such as the Rayleigh criterion. But the single-slit case is the standard starting point because it clearly shows how diffraction minima and the sinc-squared intensity envelope arise.
This calculator uses the standard ideal model. It computes minima angles, the central maximum width, and the diffraction envelope, while the interactive plot and contained animation help visualize how the pattern broadens when the slit width changes or when the wavelength changes.