Light - Part VIII

Lenses 
All of us at some time or the other have seen or used lenses. Lenses naturally occur in eyes and are a good example. If natural lenses deteriorate, extra lenses (spectacles, contact lenses) have to be added for obtaining a better vision.  Lenses are used in cameras, microscopes, binoculars and many other optical equipment.  

Lenses are optical elements used to focus or defocus images. They are generally made of high quality glass, but these days, high quality plastics or polymers are also used. The surface of a lens can be convex, concave, plane or a combination of these. A lens is not coated as a mirror, but because of the way the surface is curved, they can make light rays passing through them diverge or converge. They refract light rays and not reflect them.

There are two types of lenses : diverging or concave lens and  converging or a convex lens.

Convex Lens : A convex lens focuses light rays coming from infinite distance at its focal point. The lens is thicker in the middle. 

Concave Lens : A concave lens defocuses light rays coming from infinite distance. The parallel light rays appear to diverge from the focal point of the lens. The lens is thinner in the middle.  

Some definitions regarding convex and concave lenses

Centre of curvature : The centre of curvature of a lens is defined as the centre of the spherical surfaces  from which the lens has been cut. Thus there will two centres of curvatures. The letter C₁ and C₂ represent them.  

Aperture :  The maximum portion of the spherical surfaces from which the lens actions take place is called the aperture of the lens. In the figure, the distance AB is the aperture of the lens.  

Principal axis : The line joining the centres of curvatures is known as the principal axis of the lens. The principal axis of a spherical lens, functions similar to the normal of the plane mirror. A ray of light passing along the principle axis will not be refracted.

Optical centre : The intersection of the line joining the lens aperture and the principal axis is called the optic centre of the lens. Any ray of light passing through the optic centre emerges parallel to the direction of the incident ray. (this we shall see later). The optic centre is denoted by O.

Principal focus and focal plane :  Since a lens consists of two surfaces, there are thus first and second focus and first and second focal plane.

The principal or first focus F₁ of a convex lens is the point on the principal axis from which when the light rays start, on passing through the lens will become parallel. The second focus F₂ of a convex lens is just the opposite of the first focus, the parallel light rays impinging on the lens converge at a point on the principle axis. This point is called the second focus. The distance between the optical centre O and the first focal point is known as the first focal length f₁. The distance between the optical centre O and the second focal point is known as the second focal length f₂. Similarly, a vertical plane passing through F₁ is known as the first focal plane and a vertical plane passing F₂ through is called the second focal plane. For a symmetric convex lens f₁ = f₂ and the values are positive.  

The principal or first focus F₁ of a concave lens is the point on the principal axis from which when the light ray start, on passing through the lens will appear to become parallel rays on the same side of the light source. The second focus F₂ of a concave lens that point on the principle axis where the parallel light rays impinging on the lens appear to converge on the same side of the lens. This point is called the second focus. The distance between the optical centre O and the first focal point is known as the first focal length f₁. The distance between the optical centre O and the second focal point is known as the second focal length f₂. Similarly, a vertical plane passing through F₁ is known as the first focal plane and a vertical plane passing F₂ through is called the second focal plane. For a symmetric concave lens f₁ = f₂ and the values are conventionally taken as negative.  

Ray diagram for a convex lens : Figure below shows how light rays are focused by a convex lens.  A convex lens may be considered to be made up of two prisms and a solid glass block in the centre. Prisms divert or refract light rays toward the direction of their bases. The prisms have their bases towards the optical centre. Ray 1 is parallel to the principal axis. After passing through the upper prism, it bends towards its base and passes through the focus F. Similarly for ray 3. Ray 2 on the other hand is along the principal axis and is normal on the rectangular glass block. This ray passes un-deviated along the principal axis. All the rays meet at F. This is the reason why a convex lens is called a converging lens.  

Ray diagram for a concave lens : Figure below shows how light rays are focused by a concave lens.  A concave lens may be considered to be made up of two prisms and a solid glass block in the centre. Prisms divert or refract light rays toward the direction of their bases. The prisms have their bases away from the optical centre. The central glass block is also placed edge on. Thus the arrangements of prisms and the glass block differs considerably in a concave lens. Ray 1 is parallel to the principal axis. After passing through the upper prism, it bends towards its base and away from the principal axis. Similarly for ray 3. Ray 2 on the other hand is along the principal axis and is normal on the rectangular glass block. This ray passes un-deviated along the principal axis. All the rays appear to meet at F behind the concave lens. This is the reason why a concave lens is called a diverging lens.

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