Single-Slit Diffraction: Phasor Intensity and Pattern Width

All flashcards

Huygens source in a slit model

A small part of the slit treated as a source of a secondary wavelet.

Full-slit phase change

For slit width $a$ and observation angle $\theta$, $\phi=2\pi a\sin\theta/\lambda$.

Phasor

A vector-like representation of an oscillation's amplitude and phase.

Why is the central diffraction maximum brightest?

At $\theta=0$, the slit contributions are in phase and their amplitudes add.

Intensity at a diffraction minimum

It is zero when the resultant field amplitude cancels.

Quiz questions

1. For a slit of width $a$, wavelength $\lambda$, and observation angle $\theta$, which expression defines $\beta$?Answer: $\beta=\pi a\sin\theta/\lambda$
2. In single-slit diffraction, how is the field amplitude $E$ related to its central value $E_0$?Answer: $E/E_0=\sin\beta/\beta$
3. For which condition do single-slit diffraction minima occur?Answer: $a\sin\theta=m\lambda$, where $m$ is a nonzero integer
4. At $\beta=3\pi/2$, approximately what is the relative intensity $I/I_0$?Answer: About $0.045$
5. Which expression gives the single-slit intensity relative to the central intensity?Answer: $I/I_0=(\sin\beta/\beta)^2$