The wave equation is given by:
$$\frac{\partial^2 \psi}{\partial x^2} + \frac{\partial^2 \psi}{\partial y^2} + \frac{\partial^2 \psi}{\partial z^2} = \frac{1}{v^2} \frac{\partial^2 \psi}{\partial t^2}$$
where $\psi$ is the wave function, $v$ is the velocity of the wave and $x$, $y$, $z$ and $t$ are the spatial and temporal coordinates respectively.


The Huygens principle states that every point on a wavefront can be considered as a source of secondary spherical wavelets. These secondary wavelets combine to form the new wavefront.


Snell's law relates the angle of incidence and the angle of refraction of a wave passing through a boundary between two media with different refractive indices. The law is given by:
$$\frac{\sin \theta_1}{\sin \theta_2} = \frac{v_1}{v_2} = \frac{n_2}{n_1}$$
where $\theta_1$ and $\theta_2$ are the angles of incidence and refraction respectively, $v_1$ and $v_2$ are the velocities of the wave in the two media and $n_1$ and $n_2$ are the refractive indices of the two media.


The diffraction grating equation relates the angle of diffraction of a wave passing through a diffraction grating to the wavelength of the wave and the spacing between the grating lines. The equation is given by:
$$n \lambda = d \sin \theta$$
where $n$ is the order of diffraction, $\lambda$ is the wavelength of the wave, $d$ is the spacing between the grating lines and $\theta$ is the angle of diffraction.


Young's double slit experiment demonstrates the interference of light waves. The distance between the slits is $d$, the distance between the slits and the screen is $D$ and the wavelength of the light is $\lambda$. The equation for the location of the bright fringes is given by:
$$\tan \theta = \frac{m \lambda}{d}$$
where $m$ is the order of the bright fringe.