Thin Lenses

In order to understand lenses, one must first define some terms.

Some Definitions

The Focal point is the location at which rays parallel to the optical axis of an ideal mirror or lens converges to a point.
The focal length is the distance between the focal point and the middle of the lens. It will be represented by F. You will also see 2F being mentioned. 2F just refers to two times the focal length.
The distance from the center of the lens to the object will be referred to as d_o.
The distance from the center of the lens to the image will be referred to as d_i.
A Real Image is an optical image at which rays from the object converge. It is inverted or flipped upside down.
A Virtual Image is a point from which Light rays appear to converge without actually doing so. It is upright or in the same direction as the object.
A concave lens is a lens thinner in center than edges and is diverging.
A convex lens is a lens thicker in the center than at the edges and is converging.