What is the lens equation used to relate focal length, object distance, and image distance for a lens?

The lens equation, which is essential in optics, describes the relationship between the focal length of a lens, the distance from the lens to the object, and the distance from the lens to the image produced by that object. The equation is expressed as 1/f = 1/do + 1/di, where:

• f is the focal length of the lens,
• do is the object distance (the distance from the object to the lens),
• di is the image distance (the distance from the lens to the image).

This equation conveys that the reciprocal of the focal length is equal to the sum of the reciprocals of both the object distance and the image distance. It effectively allows one to solve for any of the three variables if the other two are known, illustrating the relationship between the object, the image created by the lens, and the lens itself.

Understanding this relationship is crucial in determining how a lens will focus light from an object at a certain distance and how it will create an image, either real or virtual. This framework is foundational in optics, providing insight into how various optical devices—like cameras, glasses, and microscopes—function.