Based on standard optical sign conventions, particularly as noted in the provided reference, the quantity that is considered negative in the context of a convex lens setup is the object distance.
Understanding Sign Conventions in Optics
In the study of lenses and mirrors, a consistent set of rules, known as sign conventions, is used to describe the positions and characteristics of objects, images, and the lens itself. These conventions help ensure that calculations using formulas like the lens equation ($\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$) yield correct results.
The Cartesian Sign Convention
A widely adopted convention is the Cartesian sign convention, which treats the lens or mirror as being located at the origin (0,0) of a coordinate system.
- Distances measured in the direction of incoming light (typically rightward) are considered positive.
- Distances measured in the opposite direction of incoming light (typically leftward) are considered negative.
- Heights measured upward from the principal axis are positive.
- Heights measured downward from the principal axis are negative.
Why is the Object Distance Negative?
According to the reference provided:
"Please note that the light rays (object distance) comes from the left side and the image is formed on the right side of the lens as convex lens always converge. It makes focal length and image distance positive for the convex lens. The object distance is negative as it is on the left side of the lens."
This statement clearly indicates that the object is conventionally placed to the left of the lens. Since the incoming light rays originate from the object and travel towards the lens from the left, distances measured to the left (where the object is located) are considered negative according to the sign convention.
Therefore, for a real object placed in front of a convex lens, the object distance ($u$) is always taken as negative.
Signs for a Convex Lens
For a convex lens, the key signs under standard conditions are:
- Focal Length ($f$): Positive. A convex lens is a converging lens, and its principal focus is on the side where the real image is formed (the right side, according to the reference).
- Object Distance ($u$): Negative. As explained above and confirmed by the reference, the object is conventionally placed to the left of the lens.
- Image Distance ($v$):
- Positive for a real image. Real images formed by a convex lens are typically on the right side of the lens.
- Negative for a virtual image. Virtual images are formed on the same side as the object (the left side).
Here's a simple summary table:
| Quantity | Symbol | Sign (for a real object) | Reason (based on convention & reference) |
|---|---|---|---|
| Object Distance | $u$ | Negative | Object is placed on the left side of the lens. |
| Focal Length | $f$ | Positive | Convex lens is converging; focus is on the right side. |
| Image Distance | $v$ | Positive (Real Image) | Real images form on the right side. |
| Negative (Virtual Image) | Virtual images form on the left side. |
In summary, within the standard sign conventions used in optics, the object distance is the primary quantity that is considered negative when dealing with a convex lens and a real object.
