Spherical lens

What is spherical lens?

Definition : A piece of a transparent medium bounded by at least one spherical surface, is called a spherical lens.

Types of spherical lenses

Types : There are two types of spherical lenses:

(I) Convex or Converging Lenses : These are thick in the middle and thin at the edges.

 

Convex or Converging Lenses
Three types of convex lenses

1. Double Convex Lens : It has both the surfaces convex.

2. Plano–Convex Lens : It has one surface plane and the other surface convex.

3. Concavo–Convex Lens : It has one surface concave and the other surface convex.

(II) Concave or Diverging Lenses : These are thin in the middle and thick at the edges.

There are three types of concave lenses :

Concave or Diverging Lenses
Three types of concave lenses

1. Double Concave Lens : It has both the surfaces concave. (Fig.)

2. Plano–Concave Lens : It has one surface plane and the other surface concave. (fig.)

3. Convexo–Concave Lens : It has one surface convex and the other surface concave. (fig.)

Some Associated terms

Centre of curvature (C)

The centre of curvature of the surface of a lens is the centre of the sphere of which it forms a part, because a lens has two surfaces, so it has two centres of curvature. In figure (a) and (b) points, C1 and C2 are the centres of curvature.

Radius of curvature (R)

The radius of curvature of the surface of a lens is the radius of the sphere of which the surface forms a part. R1 and R2 in the figure (a) and (b) represents radius of curvature.

Principal axis (C­1C2) : 

It is the line passing through the two centres of curvature (C1 and C2) of the lens.

Principal axis
Characteristics of convex and concave lenses

Optical centre :

If a ray of light is incident on a lens such that after refraction through the lens the emergent ray is parallel to the incident ray, then the point at which the refracted ray intersects, the principal axis is called the optical centre of the lens.

\frac{{O{{P}_{1}}}}{{O{{P}_{2}}}}=\frac{{{{P}_{1}}{{C}_{1}}}}{{{{P}_{2}}{{C}_{2}}}}=\frac{{{{R}_{1}}}}{{{{R}_{2}}}}

If the radii of curvature of the two surfaces are equal, then the optical centre coincides with the geometric centre of the lens.

Optical centre
Optical centre

Principal foci and focal length

First principal focus and first focal length

It is a fixed point on the principal axis such that rays starting from this point (in convex lens) or appearing to go towards this point (concave lens), after refraction through the lens, become parallel to the principal axis. It is represented by F1.

Ray diagram showing first principal focus
Ray diagram showing first principal focus
Second principal focus and second focal length :

It is a fixed point on the principal axis such that the light rays incident parallel to the principal axis, after refraction through the lens, either converge to this point (in convex lens) or appear to diverge from this point (in concave lens). It is denoted by F2.

Ray diagram showing second principal focus
Ray diagram showing second principal focus

If the medium on both sides of a lens is same, then the numerical values of the first and second focal lengths are equal. Thus

f = f’

Aperture

It is the diameter of the circular boundary of the lens.