Wellen

Waves

Diffraction experiment with waves

The following expression can be written the following expression for the general form of a wave:

f = Ae^−iwt+ikx

w=2pn: frequency of a wave
k = ^2π/_l= ^p/_h : wave vector

The intensity of a wave is given by the following quantity square: I = |φ|². The general rule for calculation of complex number c square is as follows |c|²= c·c* ; where c* is complex conjugate to complex number c; for instance complex conjugate to i is -i ( i ® -i ).

When substituting the first equation into expression for intensity one can write down: I = |φ|² = |Ae^{−i(wt−kx).} A*e^+i(wt−kx)| = |A|²

There are two waves coming from two identical slits (as it's shown on illustration) and both waves layer in detector D giving total intensity I. The intensity of two overlaped waves φ₁ and φ₂ having the same frequency but different phases is as follows Phase ist dann:

φ₁ = A₁e^−iwt+ikx and f₂ = A₂e^{−iwt+ikx+ij} where j = phase difference

I = |φ₁+φ₂|² = (φ₁+φ₂) · (φ₁*+φ₂*) = |φ₁|² + |φ₂|² + φ₁*·φ₂ + φ₁·φ₂*

I = I₁ + I₂ + A₁*A₂e^ij + A₁A₂*e^−ij

Next we can write down: A₁A₂ = (I₁I₂)^½ and
e^ix = cos x + isin x and correspondingly e^-ix = cos x - isin x, d.h. e^ij + e^−ij = 2 cos j, because
e^ij + e^−ij = cos j + isin j + cos (-j) + isin (-j) = 2 cos j

I = I₁ + I₂ + 2(I₁I₂)^½. cos j

Auf diesem Webangebot gilt die Datenschutzerklärung der TU Braunschweig mit Ausnahme der Abschnitte VI, VII und VIII.