Here we will present the New Cartesian **Sign Convention for spherical lenses** for measuring various distances in the ray diagrams of spherical lenses (convex lenses and concave lenses).

## Sign convention for spherical lenses

According to the New Cartesian Sign, the

sign Convention for spherical lensesgoes like the following:

(i) All the distances are measured from the optical centre of the lens.

(ii) The distances measured in the same direction as that of incident light are taken as positive.

(iii) The distances measured against the direction of incident light are taken as negative.

(iv) The distances measured upward and perpendicular to the principal axis are taken as positive.

(v) The distances measured downward and perpendicular to the principal axis are taken as negative.

### Sign convention for spherical lenses – explanation

The New Cartesian Sign Convention for lenses is shown in Figure 1.

The object is always placed on the left side of the lens (as shown in Figure 1) so that the direction of incident light is from left to right.

#### Distances – convention

All the distances measured from the optical centre (C) of the lens to the right side will be considered positive (because they will be in the same direction as the incident light).

On the other hand, all the distances measured from the optical centre (C) of the lens to the left side are considered negative (because they are measured against the direction of incident light).

#### focal length – convention

On the basis of New Cartesian Sign Convention, the focal length of a convex lens is considered positive (and written with a plus sign).

On the other hand, the focal length of a concave lens is considered negative (and written with a minus sign).

Please note that the sign convention for spherical lenses is very similar to the sign convention for spherical mirrors.