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Refraction by Spherical Lenses

Lenses play a very important role in our everyday life. Lenses are used in making spectacles, cameras, microscopes, telescopes, film projectors and many other optical instruments. The working of a lens is based on the refraction of light rays, when they pass through it.

Before we proceed further, let us answer the question ‘what is a lens?’ A lens is a piece of transparent glass bound by two spherical surfaces. There are two types of lenses; convex lens and concave lens.

A concave lens is thin in the middle but thicker at the edges. The given figure shows a concave lens in which the two surfaces C and D are concave or bent inward. Concave lens diverge the ray of light radiations incident on it, so it is called as diverging lens.

Several rays of light parallel to the principal axis are falling on a concave lens. These rays, after refraction from the lens, appear to diverge from a point on the principal axis. This point on the principal axis is called the principal focus of the concave lens.

 


A convex lens is thick at the centre but thinner at the edges. The given figure shows a convex lens in which the two surfaces A and B are bulging out at the centre. Convex lens converge the ray of light radiations incident on it, so it is called as converging lens.

Several rays of light parallel to the principal axis are falling on a convex lens. These rays, after refraction from the lens, converge to a point on the principal axis. This point on the principal axis is called the principal focus of the lens.

 



Refraction through Spherical Lenses
In order to discuss the formation of images by a spherical lens, it is necessary to define a few terms related to spherical lenses.

1. Optical Centre
If the lens is sufficiently thin, the rays going through the centre O of the lens, suffer negligible displacement. The centre of the lens is called its optical centre. The rays passing through O are drawn straight. 

2. Principal Axis
The line joining the centres of curvature of the two faces of the lens is called its principal axis. It passes through the optical centre. 

3. Principal Focus and Focal Length
If a parallel beam is incident on a convex (converging) lens in a direction parallel to its principal axis, after refraction through the lens, all rays converge at a point on the principal axis. This point F is called principal focus. 

In the case of a concave (diverging) lens, all rays parallel to the principal axis, after refraction through the lens, spread out and appear to diverge from its focus F behind the lens. Thus, the focus is real for a convex lens and virtual for a concave lens. Focal length f of lens is the distance between the optical centre O and focus F.

Conversely, if rays diverge from a point F' in the case of convex lens or appear to converge to a point F' in the case of a concave lens, they will be rendered parallel after refraction through the lens. Thus, by symmetry, every lens has two principal foci, one on each side of the lens and at the same distance from its optical centre. By convention, focal length f is taken to be the distance of F (not F') from O. 





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