What is the essential difference between interference and diffraction of light? None of the college textbooks I have read explains it, only Khalid's Physics explains it to the point. The book is just a few words, concise, and now I will talk about it in detail.
The amplitudes of separated waves from separated points on the same wavefront add up at the observation place to form interference; At the observation point, the amplitudes of many wavelets emitted by continuous points in a limited area on the same wavefront are continuously added point by point, which is called diffraction.
1, interference of light
The polarization of light energy proves that light is a shear wave, and its vibration displacement is perpendicular to the propagation direction of vibration dynamics. Therefore, the wave equation of light is
y==Acos 2π(υt + r/λ)
Where y is the vibration displacement, υ is the frequency, t is the time variable, r is the optical path (the distance from the light source to the observation site), λ is the wavelength, λ==c/υ, and c is the wave velocity (the speed of light).
2 π (υ t+r/λ) phase
Two waves with the same frequency and direction meet at the observation point. If the phase difference is Δ φ = = 2kπ (in-phase), the peaks meet, the valleys meet, the amplitude increases, and a bright line is formed. If the phase difference Δ φ = (2k+1) π (anti-phase), the peaks and valleys intersect, the Gu Feng intersects, and the amplitude decreases, forming a dark line, that is.
Δ φ = = 2π (R2-r1)/λ = = 2kπ, strengthening (opening)
Δ φ = = 2π (R2-r1)/λ = = (2k+1) π, weakening (dark line).
After finishing, there are
δφ=δ= R2-r 1 = = 2k(λ/2)= = kλ, strengthening (grain opening) (00 1 formula).
δ φ = δ = R2-r1= = (2k+1) (λ/2), weakening (dark line) (002 formula)
The results show that for waves with the same frequency and direction, the phase difference δ φ and the formation price of bright stripes and dark stripes are only determined by the optical path difference.
Different interference mechanisms, such as double slit interference (Pinfeld prism), thin film interference and sharp wedge interference (Newton's ring), have different expressions of optical path difference δ, but the formation rules of bright lines and dark lines are the same.
2. Diffraction of light
It has been pointed out before that at the observation point, the amplitudes of multiple wavelets emitted from continuous points in a limited area on the same wavefront are continuously added point by point to form diffraction.
The mathematical essence of point-by-point continuous addition of amplitude is integration. We adopt a simplified processing method: according to the optical path to the observation site, it is divided into several half-bands (the optical path of the same band is the same, and the optical path difference between adjacent bands is λ/2).
(1) If the number of half bands is even (2 k) and the optical path difference between adjacent bands is λ/2, the two phases cancel out, so a dark line is formed at this time, that is,
δ== 2 k(λ/2) is dark,
Note: This is the condition for interference to form bright lines.
(2) If the number of half-bands is odd (2 k+ 1), after two adjacent bands cancel each other, one band will inevitably remain, which will form a bright pattern, that is,
δ== (2 k+ 1)(λ/2) is an open pattern,
Note: This is the condition for interference to form dark lines.
The half-wave band that forms diffraction moire is only a small part of the whole beam, so diffraction moire does not interfere with the brightness of moire, which is consistent with the experimental facts and proves that the above explanation of diffraction moire formation is correct.
Interference fringe, δφ= = 2k(λ/2)= = kλ.
Brightness is independent of the number of bright patterns.
Diffraction pattern, δφ= =(2k+ 1)(λ/2)
The more series, the more half-bands. After the two phases are eliminated, the half-wave band that forms the diffraction bright pattern accounts for a small proportion in the whole beam, so the greater the number of diffraction bright patterns, the smaller the brightness (the brightness in the central bright pattern is the largest).
This is consistent with the experimental facts, which proves that the formation of diffraction bright lines explained above is correct.