Combination of thin lenses in contact

The lens is a transmitting device that focuses or scatters rays of light by suggesting refraction. A simple lens is made of a single piece of transparent material, whereas a compound lens is made up of multiple simple lenses aligned along a standard axis. A lens will focus light to form an image, as opposed to a prism, which will refract light while not focusing. In combination with thin lenses in contact, we use two types of lenses. These two thin lenses are concave lens and convex lens. 

A transparent object that is shaped to bend light rays in a particular way as it passes through it, means that the rays converge or diverge at a particular point such as  from a particular point. The object may be a piece of plastic or glass, and the shape of the lens causes the light rays to converge or to diverge. The word lens is derived from Latin for lentil which means the shape between the converging lens and the legume.

The difference in the index of refraction of the lens with surrounding air causes the light rays to bend. This phenomenon is represented by Snell’s law of refraction.

Some unique terms associated with the lenses

Focal point– The parallel rays after passing through the lens converge at a point known as the focal point.

Focal length– It is the distance from the focal point to the centre generally known as the bending power of the lens.

Optical axis– It is a line of symmetry of the lens.

Ray of light– A ray of light is the path of light in which straight lines are used to illustrate the motion of light waves. 

Optical lens– An object that is shaped in such a way that it makes the light rays diverge or converge is known as an optical lens. For converging, the convex lens is used, and for diverging, the concave lens is used.

Biconcavelens– An object with the optical lens of two convex sides is generally known as a convex-convex lens and is characterised by a positive focal length. It is basically used in microscopes and telescopes.

Depth of field– When viewed through the lens the distance at which the object is seen to be in focus. For example, in photography. The range of focus is the depth of field.

Prime lens– This lens is widely used in photography having a fixed focal length, as opposed to the zoom lens where the focal length can be altered. In another way, we can say the prime lens can be used to mean the primary lens in the composition of multiple lenses.

Power of lens:– It is the process of determining the degree of convergence or divergence of the light that falls on it. It is denoted by the letter P. It is defined as the reciprocal of the focal length process. Dioptre is the unit of power of the lens, which is denoted by the letter D.

Mathematical concepts

In combination with thin lenses in contact:- We use two types of lenses similar or dissimilar.  Let’s assume two lenses, lens A and lens B of focal length f1 and f2 kept in touch with each other. An object is kept at O on the common principal axis. We assume that lens A produces an image at I1. Its image I1acts as the object for the second lens B. The final image is produced at I. 

Convex lenses are also known as converging lenses. These lenses have a thicker centre and a thinner end. It is a converging lens because the light rays are bent inward and converge to some extent, which is understood as the focal length.

A diverging lens is another name for a concave lens. These lenses have a flat centre and are thicker at the edges. It is a diverging lens because it bends parallel light rays from outside and diverts them to the focal point.

Let’s assume PO = u, object distance for the first lens A, 

PI = v, final image distance and 

PI1 = v1, image distance for the first lens A and also object distance for second lens B

For the image I1, produced by the first lens A,

1/v1 – 1/u = 1/f1 …………….(1)

For the final image I, produced by the second lens B,

1/v – 1/v1 = 1/f2 …………….(2)

Adding equations 1 and 2

1/v – 1/u = 1/f1 + 1/f2 ………..(3)

If the combination is replaced by a single lens of focal length F, it forms an image of O at the same position I, then

1/v – 1/u = 1/f…………..(4)

From equations 3 and 4 is

I/f = 1/f1 + 1/f2………….(5)

This F represents the focal length of the combination’s equivalent lens.

Power of lens is

P = 1/f

According to equation 5,

Conclusion

In combination of thin lenses in contact, we use two types of lenses. These two thin lenses are diverging lenses and converging lenses. It is a mixture of various simple lenses. The combination of thin lenses is used in many optical instruments such as microscopes, cameras, telescopes, etc. This combination of thin lenses is necessary because it develops the magnification of the image, sharpness of the image, and forms the ultimate image erect, etc.