This is a list of commonly used formulas and diagrams used in Geometrical Optics. The sign convention follows the one adopted by the College of Optical Sciences at the University of Arizona. For a more complete list and guide please refer to “Field Guide to Geometrical Optics” by J.E. Greivenkamp.

• Snell’s law of refraction:

• Total internal reflection (TIR):

subject to

• Power of an optical surface:

• Curvature:

• Effective Focal Length:

• The front and rear focal lengths are related to the EFL:

• Reflective surfaces:

In a reflection $$n’ = -n$$

• Gaussian Equations:

• Longitudinal magification:

As the plane seperation goes to zero, the local longitudinal magnification is obtained:

• Gaussian reduction:

Gaussian reduction is the process of combining elements two at a time into a single equivalent focal systems

$n_2$ is the index of refraction of the space between the front and rear principal planes

$\phi$ is the power of the combined system

$\phi_1$ is the power of the first element or system

$\phi_2$ is the power of the second element or system

$d$ is the shift in object space of the front system principal plane

$d'$ is the shift in image space of the rear system principal plane

$t$ is the directed distance in the intermediate optical space from the rear principal place of the first system to the front principal plane of the second system.

• Power of a thin lens in air:

The principal planes and nodal points are located at the lens.

• Vertex distances:

Back focal distances is the distance from the rear vectex to the rear focal point.

Front focal distance is the distance from the front vertex to the front focal point.

• Paraxial optics:

Refraction (and reflection):

Transfer:

• Rear Cardinal Points:

Trace a ray parallel to the axis in object space ( $u = \omega = 0$ ). This ray must go through the rear focal point $F'$

• Front Cardinal Points:

Trace a ray from the system front focal point $F$ that emerges parallel to the axis in image space. The reverse raytrace equations are used to work from image space back to object space.