Is the Focal Length of a Convex Lens Positive or Negative?

The focal length ($f$) of a Convex Lens is Always Positive (+).

• If a physics problem states: 'A convex lens has a focal length of 20 cm', you must write it in your formula as $f = +20 \text{ cm}$.

In optics, we strictly follow the 'New Cartesian Sign Convention' (which works exactly like an X-Y graph in math).

1. We place the optical center of the lens at the origin (0,0).
2. We assume that the ray of light is always travelling from Left to Right.
3. The Rule: Any distance measured to the Right of the lens (in the direction of the light) is taken as Positive (+).

When parallel light rays pass through a Convex Lens, the lens 'converges' (bends) them all to meet at a single focus point on the Right side of the lens. Because the primary Principal Focus ($F_2$) lies on the right side, the distance to it is logically measured as Positive.

By the exact same logic, a Concave Lens scatters light. The light rays appear to meet at a focus point on the Left side (behind the light source). Since it is on the left side, the focal length of a Concave Lens is Always Negative (-).