Cartesian Sign Convention

A sign convention must be defined, understood, and followed. The Cartesian sign convention will be used in this course. This is NOT the same as used in Halliday and Resnick, but is used in many specialist optics textbooks. In this case we have:-

1) Light initially propagates from left to right.

2) The origin of the Cartesian coordinate system is at the centre of the optical component.

3) Distances measured normal to the optic axis are positive above and negative below.

4) We denote object space distances as l, h, f, and image space distances as l ', h', f '.

5) Acute angles are positive when produced by anticlockwise rotation from the optic axis, and negative when produced by clockwise rotation.

Figure 2. The Cartesian sign convention

Let us take as an example an object 10 cm to the left of a converging lens of focal length 5 cm.

• In this case the object distance is l (lower case L) and is negative, as it is to the left of the "origin" of the axes.
• The focal length of the lens is positive.
• The image is formed 10 cm to the right of the lens. This means that the image distance, l', is positive.

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