Spherical Lens

LENSES:

A lens is a portion of a transparent  medium (such as glass) bounded by two spherical surfaces .

Lenses are  two types : 

(1) Convex lens or converging lens 

(2) Concave lens or diverging lens 

1. Convex lens or converging lens. 
A convex lens is thicker in the middle than at the edges. It converges (i.e. brings together) parallel rays of light on refraction through it.

 Convex lenses are of three types.

Types of convex lens

 (i) Double convex lens:  Both surfaces are convex 
 (ii) Planoconvex lens - One surface convex 'and other plane
 (iii) Concavoconvex  lens :  One surface is convex and the other concave

converge  parallel rays of light

2: Concave lens or diverging lens.

A concave lens is thinner at the centre than at the edges.
It diverges (i.e. spreads out) parallel rays of light on refraction through it.

Concave lenses are of three types

(i) Double concave lens:  Both surfaces are concave
 (ii) Plano concave lens - One surface concave 'and other plane
 (iii) Concavoconvex  lens :  One surface is convex and the other concave

Few Basic Terms Related to Spherical Lens

1. Centre of curvature : A lens, either a convex lens or a concave lens is combination of two spherical surfaces. Each of these surfaces forma part of sphere. The centre of these two spheres are called centre of curvature represented by C1 and C2.
2. Principal axis :Imaginary straight line passing through the two centres of curvature
3. Optical Centre : The central point of lens is its optical centre (O). A ray of light, when passes through ‘O’ it remains undeviated i.e. it goes straight.
4. Aperture : The effective diameter of the circular outline of a spherical lens.
5. Focus of lens : Beam of light parallel to principal axis, after refraction from

1. Convex lens, converge to the point on principal axis, denoted by F, known as Principal focus

2. Concave lens, appear to diverge from a point on the principal axis known as principal focus.

The distance OF2 and OF1 is called as focal length

Tips for Drawaomg Ray Diagram

1. After refraction, a ray parallel to principal axis will pass through F.
2. A ray passes through F, after refraction will emerge parallel to principal axis
   

Image formation by a convex lens for various position of object

Image Formation by Concave Lens

NEW CARTESIAN SIGN CONVENTION

While dealing with refraction  at lens , the following sign convention called New Cartesian Sign Convention is followed : 

(i) All distances are measured from the optical center  of the lens. 

(ii) The distances measured in the direction of the incident light are taken as positive while those measured in the direction opposite to the incident light are taken as negative.

 (iii) Heights or distances measured upward and perpendicular to the principal axis are considered positive while those measured downwards are considered negative. 

According to this sign convention, the focal length (f) is  positive  for a convex lens  and negative  for a concave  lens.

Lens formula