Why is u Always Negative?

Step 1: In the Cartesian system, we place the optical element (mirror or lens) at the origin.

Step 2: Incident light travels from left to right. This defines the positive x-direction.

Step 3: The object is always placed to the left of the optical element (so that the incident light can actually hit the element).

Step 4: "To the left" is opposite to the positive x-direction (opposite to incident light direction).

Step 5: By convention, distances measured opposite to the direction of incident light are NEGATIVE.

Conclusion: The object distance u is measured from the optical element to the object, which is to the left — hence u is always negative for real objects. ✓