Crossed Beams

Beams crossing at an angle result in Interference Fringes at their intersection

$$E_1+E_2=E_0\exp i(kz\cos \theta +kx\sin \theta -\omega t)+\exp i(kz\cos \theta -kx\sin \theta -\omega t)$$ $$⟹E(x,z,t)=E_0\exp \left(i(kz\cos \theta -\omega t)\right)(2\cos kx\sin \theta )$$ $$⟹I(x,t)\propto 4I_0{\cos }^2(kx\sin \theta )=2I_0(1+\cos (2kx\sin \theta ))$$

• Fringe Spacing, $\Lambda$

See Also

Michelson Interferometer/Michelson-Morley Experiment