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# Spherical Lenses – Definition, Terms Related to Spherical Lenses

## Spherical Lenses

### Introduction

All transparent materials refract light. For example, a glass slab refracts light. There are many other commonly found objects in our surroundings that also refract light, such as the glass bodies of a magnifying glass, the glass body of the spectacles, the binoculars etc. These objects when touched are not of uniform thickness like a glass slab, but  have varying thickness. Some are thicker in the middle and thinner towards the edges and vice versa. These transparent objects are called lenses. In this section we will be throwing some light on the way these lenses refract light.

### Spherical lenses:

A transparent material bound by two surfaces of which one or both surfaces are spherical, forms a lens. They are widely used in spectacles, microscopes and telescopes.

A transparent material bound by two bulged out spherical surfaces is called a biconvex lens or simply convex lens. A transparent material bound by two curved in spherical surfaces is called a biconcave lens or simply concave lens. A convex lens is thicker in the middle and thinner towards the edges. However, a concave lens is thinner in the middle and thicker towards the edges.

#### Terms related to spherical lenses:

• Both concave and convex lenses have two curved surfaces, each of which forms a part of a sphere. The centers of these spheres are called the centers of curvature of the surfaces, C1 and C2
• An imaginary straight line passing through the two centers of curvature of a lens is called its principal axis
• The central point of a lens is called its optic center (O)
• The diameter of the circular outline of a lens is called its aperture.
• When a parallel beam of light falls on a convex lens, it converges to a point after refraction. This point F is called the focal point or focus of a convex lens. As a parallel beam of light converges to a point after refraction through a convex lens, it is also called a converging lens
• When a parallel beam of light falls on a concave lens, it diverges in such a way that it appears to diverge from a point (F) after refraction. This point F is called the focal point or focus of a concave lens. As a parallel beam of light diverges after refraction through a concave lens, it is also called a diverging lens

• A lens has two principal foci represented by F1 and F2.
• The distance of the optical center from F1 or F2 represents the focal length (f) of the lens.
• The distance of the optical center from C1 or C2 represents the radius of curvature (R) of the lens.

### Relationship between R and f:

The radius of curvature of a spherical lens is twice the focal length of the lens.

That is, R = 2f

### Comparison between refraction through glass slab and spherical lenses:

• The incident rays and the emergent rays are not parallel to each other unlike refraction through a glass slab.
• The light ray in the middle passes through the optic center, hence it goes without any deviation from its usual path similar to the normal incidence during refraction through a glass slab.

## Summary

1. Lenses are transparent objects made up of a transparent material such as glass
and clear plastic. They are widely used in spectacles, microscopes and telescopes.
2. A convex lens is thicker in the middle and thinner towards the edges. However, a
concave lens is thinner in the middle and thicker towards the edges.
3. The centers of the spheres of origin of the surfaces are called their centers of
curvatures.
4. An imaginary straight line passing through the two centers of curvature of a lens
is called its principal axis. The central point of a lens is called its optic center (O).
5. The diameter of the circular outline of a lens is called its aperture.
6. The point where a parallel beam of light converges after passing through a convex
lens or the point from where a parallel beam of light appears to diverge after
passing through a concave lens is called their focal points or focus.
7. The distance between the focus and the optic center is called the focal length of a
lens.
8. The focal length and the radius of curvature of a lens are related as, R=2f.
9. A convex lens can be used to light up a fire by concentrating the sun’s rays onto its
focal point.

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