# What is a single slit

1. Jul 24, 2014

### Greg Bernhardt

Definition/Summary

This entry describes diffraction of a wave when it passes through a single narrow slit.

Equations

The far-field (Fraunhofer) diffraction pattern has a power per area (irradiance) at an angle $\theta$ from a single slit of width $d$, for wavelength $\lambda$ and wavenumber $k\ =\ 2\pi/\lambda$ of:

$$I(\theta)\ =\ \left( \frac{\sin \beta}{\beta}\right)^2\,I(0)$$

where:
$$\beta\ \equiv\ \frac{\pi d}{\lambda} \ \sin\theta\ =\ \frac{k d}{2} \ \sin\theta$$

which for very small angles is approximately:
$$\beta \ \approx \ \frac{\pi d}{\lambda} \ \theta \ = \ \frac{kd}{2} \ \theta$$

The diffraction minima (dark fringes) occur when

$$\beta \ = \ n \pi, \ \ n \ = \ \pm 1, \ \pm 2, \ \pm 3, \ ...$$

or, for small angles,

$$\theta \ \approx \ n \lambda / d, \ \ n \ = \ \pm 1, \ \pm 2, \ \pm 3, \ ...$$

Note that n=0 corresponds to the central maximum, not a minimum.

Extended explanation

Definition of terms
I = irradiance of the wave, with SI units of W/m2
I(0) = the irradiance at θ=0
d = the slit width
λ = the wavelength of the wave
k = 2π/λ
θ = the angle at which the irradiance is evaluated

* This entry is from our old Library feature, and was originally created by Redbelly98

Last edited by a moderator: Jul 27, 2014