Single-slit diffraction

Also called Single slit diffraction pattern

Single-slit diffraction is the banded pattern monochromatic light produces after passing through one narrow opening of width a. The condition printed on the AP Physics 2 sheet locates the dark fringes of that pattern, not the bright ones.

EK 14.7.A.4 names every symbol you will need: monochromatic light of wavelength $\lambda$ incident on a narrow opening of width $a$ that is a distance $L$ from a screen. EK 14.7.A.4.i explains the bands as constructive and destructive interference of multiple wavefronts originating from the opening, which is worth pausing on. One slit, and still interference, because EK 14.7.A.3 treats the opening as a source of many wavefronts rather than one.

Two printed forms, both for minima.

\Delta D = a\sin\theta = m\lambda \qquad a\frac{y_{\text{min}}}{L} \approx m\lambda

Here $\theta$ is the angle between the direction of propagation and the normal to the opening (14.7.A.4.iii), and EK 14.7.A.4.iv defines $y_{\text{min}}$ as the distance from the middle of the central bright fringe to the $m$ th order of minimum brightness, valid for $\theta < 10$ degrees. The subscript is the sheet telling you which fringe you have found. Orders run $m = 1, 2, 3$ and upward with no $m = 0$ , since the centre of the pattern is bright.

The width runs the pattern backwards. With $y_{\text{min}} \approx m\lambda L/a$ , halving the slit width doubles the spread. EK 14.7.A.2 gives the qualitative version: diffraction is most pronounced when the size of the opening is comparable to the wavelength.

Shape matters too. EK 14.7.A.5: the diffraction pattern produced by a wave passing through an opening depends on the shape of the opening. A slit and a circular hole do not give the same figure. The diffraction entry covers the phenomenon in general.

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