Single-Slit Diffraction: Pattern and Minimum Condition

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What is diffraction?

Diffraction is the bending and spreading of a wave around the edges of an opening or obstacle.

When is diffraction especially noticeable?

When the size of an opening or obstacle is comparable to the wavelength.

What does Huygens’s principle say about a wavefront?

Each point on a wavefront acts as a source of secondary wavelets.

What are the main features of a single-slit pattern?

A broad, bright central maximum and narrower, dimmer side maxima.

What condition gives the dark minima for a single slit?

For nonzero integer order $m$, minima occur when $a\sin\theta=m\lambda$.

Quiz questions

1. For a slit of width $a$, wavelength $\lambda$, and minimum angle $\theta$, which equation gives the single-slit minima?Answer: $a\sin\theta=m\lambda$, where $m$ is a nonzero integer.
2. In the single-slit minimum condition, what does $m=0$ represent?Answer: The forward direction, which is the central maximum rather than a dark minimum.
3. At the first dark minimum of a single slit, what path difference separates paired points in opposite halves of the slit?Answer: One-half wavelength, so the paired contributions arrive out of phase.
4. How are the dark minima positioned on opposite sides of the forward direction?Answer: Minima of the same order occur at equal angles on opposite sides.
5. For a proposed single-slit minimum of order $m$, what condition must hold for a real angle $\theta$?Answer: $\left|\frac{m\lambda}{a}\right|\leq 1$.