Lenses are the most used things in optical devices like microscopes and telescopes. Bi-convex and bi-concave lenses are the most popular ones in use among school labs. Lenses use the phenomenon of refraction of light to form images.
The geometric centre of a lens is called its optic centre. The line passing through the optic centre and perpendicular to the plane of the lens is the principal axis. A light ray incident on a lens, after refraction appears to emanate from the principal focus in the case of a concave lens and passes through the focus in the case of a convex lens. The diameter of the lens gives the measure of its aperture.
If a light ray parallel to the principal axis passing through the lens passes (for a convex lens) or appears to pass (for a concave lens) through the focus, it is called second principal focus. If the light ray passing through the focus (for a convex lens) or directed towards the focus (for a concave lens) after refraction through the lens passes parallel to the principal axis, the focus is the first principal focus.
Concave lens diverge the light incident on it. Hence, called the diverging lens. Due to this these lenses always form diminished, virtual and erect images irrespective of the position of the object in front of them. Thus, the magnification produced by these lenses is always less than one.
Convex lenses converge the light and hence are called the converging lenses. You can observe the magnified image of your palm when the lens is placed close to your palm. This is due the position of the object between the focus and the optic centre. As the object moves away from the lens, the size of its image reduces along with its distance from the lens. Convex lenses form erect, virtual, magnified images or inverted, real, diminished/magnified images depending on the position of the object.
The distance from the principal focus to the optic centre of the lens is the focal length of the lens.
The relation between the focal length (f), object distance (u) and the image distance (v) is given by 1/f = 1/v - 1/u.
All the distances are measured from the optic centre. If we measure the distances in the direction of the incident light, then they are taken positive and else they are taken negative. These constitute the sign conventions.