Question

Why is object distance is considered negative while measuring optical distances?

Answer 1

Sign convention:

The sign convention is a set of rules to set signs for image distance, object distance, focal length, etc for mathematical analysis of image formation.

Explanation:

1. The object is always placed to the left of the lens.
2. There is a pole in the mirror from which the distances are measured.
3. Distances measured in the direction of the incident ray are positive and the distances measured in the direction opposite to that of the incident rays are negative.
4. Distances measured along the y-axis above the principal axis are positive and that measured along the y-axis below the principal axis are negative.
5. For instance, the focal length of the concave mirror is negative as it is being measured from the optical center in the opposite direction of the incident rays.

Because the rays of a concave mirror converge at a position upon that negative side of the origin, the overall focal length of the concave mirror is negative.

Hence, the object distance is always negative while measuring optical distances according to the sign conventions.