Double slit experiment

A second narrow slit is introduced in the solid barrier. Now when the plane waves strike the barrier, circular waves are emitted from both slits. These two circular waves interfere with each other on the right side of the barrier.

Simulation details (optional)

A wave train five wavelengths long strikes a barrier and reflects off of it. Circular waves radiate from the slits.

The interference pattern on the left of the barrier is decribed by the superposition of a right moving plane wave, a left moving plane wave, and two circular waves from the slits.

$$z = -H(\xi_R+10\pi)\sin(\xi_R)H(-\xi_R) -H(\xi_L+10\pi)\sin(\xi_L)H(-\xi_L) +H(\xi_{c1}+10\pi)\frac{\sin(\xi_{c1})}{\sqrt{r_1}}H(-\xi_{c1})+H(\xi_{c2}+10\pi)\frac{\sin(\xi_{c2})}{\sqrt{r_2}}H(-\xi_{c2}),$$

where $k$ is the wavenumber, $\omega$ is the angular frequency, $r_1 = \sqrt{(x-L/2)^2+(y-L/3)^2}$ is the distance from slit 1, $r_2=\sqrt{(x-L/2)^2+(y-2L/3)^2}$ is the distance from slit 2, $\xi_R = kx -\omega t$, $\xi_L = 10\pi-kx -\omega t$, $L=5\lambda=10\pi/k$ is the length of the wavetrain, $\xi_{c1} = kr_1-\omega\left(t-\frac{L}{2}\frac{k}{\omega}\right)$, $\xi_{c2} = kr_2-\omega\left(t-\frac{L}{2}\frac{k}{\omega}\right)$, and $H(x)$ is the Heaviside function.

The circular waves on the right side of the barrier are described by,

$$z = -H(\xi_{c1}+10\pi)\frac{\sin(\xi_{c1})}{\sqrt{r_1}}H(-\xi_{c1})-H(\xi_{c2}+10\pi)\frac{\sin(\xi_{c2})}{\sqrt{r_2}}H(-\xi_{c2}).$$






	Physik für Geodäsie 511.018 / Physik M 513.805