Gen Phys 2

Interference

Interference from two sources

\begin{equation} d \textnormal{ sin } \rho = m \, \lambda \quad (m \in \mathbb{Z}) \qquad \textnormal{(Constructive interference)} \end{equation} \begin{equation} d \textnormal{ sin } \rho = \left( m + \frac{1}{2} \right) \lambda \quad (m \in \mathbb{Z}) \qquad \textnormal{(Destructive interference)} \end{equation} \begin{equation} z_m = R \, \frac{\lambda \, m}{d} \qquad \textnormal{(Fringes)} \end{equation}

Intensity of interference patterns

\begin{equation} E_p = 2 \, E \, \vert \textnormal{cos } \frac{\alpha}{2} \vert \end{equation} \begin{equation} I = I_0 \textnormal{ cos}^2 \frac{\alpha}{2} \end{equation} \begin{equation} \alpha = \frac{2 \, \pi}{\lambda} (r_2 - r_1) = k \, (r_2 - r_1) \end{equation}

Interference of thin films

\begin{equation} 2 \, t = m \, \lambda \quad (m \in \mathbb{W}) \qquad \textnormal{(Constructive reflection from thin film, no relative phase shift)} \end{equation} \begin{equation} 2 \, t = \left( m + \frac{1}{2} \right) \lambda \quad (m \in \mathbb{W}) \qquad \textnormal{(Constructive reflection from thin film, half-cycle phase shift)} \end{equation} \begin{equation} 2 \, t = \left( m + \frac{1}{2} \right) \lambda \quad (m \in \mathbb{W}) \qquad \textnormal{(Destructive reflection from thin film, no relative phase shift)} \end{equation} \begin{equation} 2 \, t = m \, \lambda \quad (m \in \mathbb{W}) \qquad \textnormal{(Destructive reflection from thin film, half-cycle phase shift)} \end{equation}