For a convex lens, how is the focal length (f) designated in the lens equation?

In the context of optics, particularly when dealing with convex lenses, the focal length is always designated as a positive value. This positive designation comes from the way light behaves when it passes through a convex lens.

A convex lens converges light rays that are parallel to its principal axis; these rays are brought together at a point called the focal point. The distance from the lens to this focal point is the focal length, which is defined to be positive. This is in contrast to concave lenses, which diverge light rays and have a negative focal length.

The lens equation itself, which is typically written as ( \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} ), utilizes the convention that the focal length (f) for a convex lens is a positive number. This conforms to the sign conventions used in optics, where distances measured in the direction of the incoming light are considered positive.

As a result, understanding this convention is crucial for solving problems related to lens behavior and image formation effectively, reinforcing the principle that a convex lens, by its nature, has a positive focal length.