sign conventions

In order to achieve similar optical formulas across various authors, an agreement on some sign convention is necessary:


The z-axis of a system is the optical axis.
As usual we assume thet the light passes from left to right through the lens elements.
Initially the light travels from -z to +z

The y-Axis is perpendicular to the z-axis and in the plane of the monitor/papersteht
The x-Axis is perpendicular on the z-axis and the y-axis and is drected into the screen/paper.

The first optical surface then has the radius R1 and the second optical surface has the Radius R2, where infinit values signal plano surfaces (blue colors in the graphic).

If the light first meets the optical surface and then the center of curvature then the radius has a positive sign, (green color arcselse a negative sign (red color arcs).

R_a above is positive and R_b is negative.

Angles are measures between the optical axis and the beam, where the smaller of the two intersection angles is used.
Incident angles are measured between the surface normal and the incident beam.

signs of refraction indices are negated after a reflection.

[table caption=”sign conventions” width=”500″ colwidth=”40|20|100″ colalign=”left|center|left”]
object distance,+,object is left of the refracting surface
object distance,-,object is right of the refracting surface
image distance,+,image point is right of the refracting surface
image distance,-,image point is left of the refracting surface
radius of curvature,+,center is right of the refracting surface
radius of curvature,-,center is left of the refracting surface
focal length (object side), +, left of the lens
focal length (image side), -, right of the lens
object distance from focal point F,-,left of object side focal point
image distance from focal point F’,+,right of image side focal point
object height,+,above optical axis
object height,-,below optical axis
angle,+,measured counterclockwise
angle,-,measured clockwise