A path length difference equal to λ causes a phase shift of 2π (360°). A path length difference of 1/2λ causes a phase shift of π (180°).
When light reflects from a boundary with a slower medium (higher index of refraction), it is inverted (180° phase change); when light reflects from a faster medium (lower index of refraction), it is not inverted (no phase change).
The angles at which the maxima and minima occur in a two-slit interference experiment are
Maxima: d sin θ = mλ (m = 0, ±1, ±2, …)
(25-10)
Minima: d sin θ = (m + 1/2)λ (m = 0, ±1, ±2, …)
(25-11)
The distance between the slits is d. The absolute value of m is called the order.
A grating with N slits produces maxima that are narrow (width ∝ 1/N) and bright (intensity ∝ N2). The maxima occur at the same angles as for two slits.
The minima in a single-slit diffraction pattern occur at angles given by
a sin θ = mλ (m = ±1, ±2, ±3, ...)
(25-12)
A wide central maximum contains most of the light energy. The other maxima are approximately (not exactly) halfway between adjacent minima.
The first minimum in the diffraction pattern due to a circular aperture is given by
a sin θ = 1.22λ
(25-13)
Rayleigh's criterion says that two sources can just barely be resolved if the center of one diffraction pattern falls at the first minimum of the other one. If Δθ is the angular separation of the two sources, then the sources can be resolved if
a sin Δθ ≥ 1.22λ0
(25-14)
The regular arrangement of atoms in a crystal makes a grating for X-rays. We can think of the X-rays as if they reflect from planes of atoms. Constructive interference occurs if the path difference between X-rays reflecting from an adjacent pair of planes is an integral multiple of the wavelength.
A hologram is made by illuminating the subject with coherent light; the hologram is a record of the intensity and the phase of the light incident on the film. The hologram recreates wavefronts just as if they were coming from the object.
