Geometric optics

Lateral magnification

\begin{equation} m = \frac{y \, '}{y} \qquad \textnormal{(Magnification)} \end{equation}

Plane mirror

\begin{equation} \frac{1}{ob} + \frac{1}{i} = 0 \qquad \textnormal{(Ob = object distance, i = image distance)} \end{equation} \begin{equation} m = - \frac{i}{ob} = 1 \qquad \textnormal{(Magnification)} \end{equation}

Sign conventions

• ob > 0 when object is on the incoming side of the surface. This is a real object.
• i > 0 when image is on the outgoing side of the surface. This is a real image.
• m > 0 when image stands right-side up; m < when image is inverted.
• R (radius of curvature) > 0 when center of curvature is on the outgoing side of the surface.

Spherical mirror

\begin{equation} \frac{1}{ob} + \frac{1}{i} = \frac{2}{R} = \frac{1}{f} \qquad \textnormal{(R = radius of curvature, f = focal length)} \end{equation} \begin{equation} m = - \frac{i}{ob} \qquad \textnormal{(Magnification)} \end{equation}

Plane refracting surface

\begin{equation} \frac{n_a}{ob} + \frac{n_b}{i} = 0 \end{equation} \begin{equation} m = - \frac{n_a \, i}{n_b \, ob} = 1 \qquad \textnormal{(Magnification)} \end{equation}

spherical refracting surface

\begin{equation} \frac{n_a}{ob} + \frac{n_b}{i} = \frac{n_b - n_a}{R} \end{equation} \begin{equation} m = - \frac{n_a \, i}{n_b \, ob} \qquad \textnormal{(Magnification)} \end{equation}

Thin lenses

\begin{equation} \frac{1}{f} = \frac{1}{i} + \frac{1}{ob} \qquad \textnormal{(Focal length, image, and object distance in a thin lense)} \end{equation} \begin{equation} \frac{1}{f} = (n - 1) \left( \frac{1}{R_1} + \frac{1}{R_2} \right) \qquad \textnormal{(Focal length, index of refraction, and radii of curvature)} \end{equation}

Camera

\begin{equation} f_{\textnormal{num}} = \frac{f}{D} \qquad \textnormal{(Light gathering capability, f = focal length, D = aperture diameter)} \end{equation}