Definition of a Lens in Optics
A lens is a transparent, optical device that stays on the laws of refraction and is used for multipurpose in physics and engineering. Being made up of plastic or glass they are also slightly curved at their surface which makes the light bend while entering them. Thus, images are either focused at a point or diverged from that point depending upon the curvature present in the lens. We are familiar with the eyeglasses which we use to correct our eyesight. Other simple examples using lenses are the cameras, microscopes etc.
Lenses are mainly: convex lenses and concave lenses, which are also called converging and diverging lenses respectively. They are categorized on the basis of their surface, either curved inward or bulged outward. All the works of correction, magnification, image projection etc. keep lenses as their fundamental element. Hence we can say optics heavily demand for lenses to perform its tasks. Modern technologies in optics and high level photography are impossible without lenses. Thus, lenses are the critical components that help to regulate light in a desirable manner.
Convex (Converging) vs Concave (Diverging) Lenses
The shape of lenses make them differ in two different ways. A convex lens, also called a converging lens, has its center quite thicker than its edges. This feature makes the incident parallel rays of light curve inward and come together at a point called the principal focus. Thus, the curving nature is highly useful in magnifying images. The glasses of microscopes, telescopes are convex lenses as they have to magnify images of small objects. It can produce both real and virtual images at certain criterias.
Likewise, a concave lens, or diverging lens, is slightly thicker at the edges and narrower at the center. This shape makes the parallel rays of light spread out and hence diverge away, leaving the impression as if they originated from a point behind the lens. They always produce virtual, upright, and smaller images. Their wide application is in the vision correction of myopia. Understanding lenses properly lies in the proper study of lenses and the ability to distinguish them accurately.
Key Lens Parts: Optical Axis, Principal Focus, Focal Length
There are several optical terms which should be known for gaining โlensesโ. They are listed below:
Optical axis: The optical axis is a reference point from which the ray of light passing through the lens is analyzed. It is an imaginary straight line running through the center of the lens and is perpendicular to its surfaces.
Principal focus: It is also called the focal point where the light rays after passing through the lens, tend to converge (in convex lens) or from where they appear to move out (for concave lens). The focal points can be on both sides of a lens since light can travel in either direction.
Focal length: It is the distance of focus from the center of the lens (optical center). Focal length is the major entity whose measurement is useful to know how strong is the nature of convergence or divergence of light.
On a broader look, the surface of a lens is the part of a sphere and two spherical surfaces whose small potions are combined to form one lens. Other terms like centre of curvature and radius of curvature are also used in lenses. Centre of curvature is the centre of that sphere resembling the distinct surface of the lens. Radius of curvature is the line joining the centre of curvature and the vertex of the surface of the lens. Recognizing the proper focal length improves the creation of optical instruments, ray diagrams, and magnification. They are the fundamental study before heading towards the lens.
Lensmakerโs Formula for Calculating Focal Length
The Lensmakerโs Formula does the calculation of focal length which requires the refractive index of that lens medium and the radii of curvature of both surfaces of the lens for the measurement. It is the major formula governing optical devices which is given by:
1/f=(ฮผโ1)(1/R1โ1/R2) [Equation 1]
Where:
- f is the focal length of the lens
- โฮผโ, the refractive index of the lens
- R1 and R2 the radii of curvature of the two lens
This formula assumes that the lens is in the air and is sufficiently thin so that computations are simple, not affected by the thickness. However, sign convention should be greatly cared for because a convex surface has a positive radius, while a concave surface has an opposite one.
All the technologies like cameras, spectacles, and microscopes are based on the Lensmaker’s Formula. The mathematical calculation also helps in treating vision problems and obtaining the appropriate image qualities. By linking a pure optical behavior to mathematics and also to physics, this mathematical tool has shaped the process of lens design.
Image Formation by Thin Lenses and Ray Diagrams
Ray diagrams are often taken to illustrate the geometry of the object position and the image position. The path of light is illustrated in a ray diagram. For example, in case of convex lenses, if the object is kept beyond the focal point on the first side its real and inverted image is obtained on the other side. To locate the image in the exact position and study its nature, three major rays are drawn which are:
- A ray parallel to the optical axis and getting refracted through the focal point.
- A ray through the focal point emerging parallel to the axis.
- A continuous ray through the center passing straight without bending.
Some ray diagrams for convex and concave lenses are given below:
Source: sarthaks.com
Ray diagrams are very essential to analyze the position of an object before constructing any optical devices. Students are also made to draw the ray diagrams while studying about lenses.
Lens Aberrations: Chromatic, Spherical, Astigmatism
Lens aberrations means the errors of lenses while focusing light. Hence, this results in blurred or distorted images. This is a major problem in lenses which occurs due to the improper design or shaping of lenses. The common types of aberrations are given below:
- Chromatic aberration arises as the lens is not properly constructed and disperses the incoming light rather than focusing them at a point. This produces colored fringes around the object and the image cannot be viewed clearly. This can be corrected by using special glass or using achromatic lenses (combination of multiple lenses of different refractive indices)
- Spherical aberration is the defect where, in comparison to rays traveling through a circular zone around the lens’s rim, those traveling through the center of the lens are focused farther away. Thus, the image produced by spherical aberration becomes unsharp. This can often happen with the lenses at larger apertures. Therefore, smaller apertures are preferred which can reduce the defect.
- Astigmatism occurs when two refracting surfaces of a lens have differing focal points. This gives stretched, elongated, diminished or images of the object. Cylindrical lenses can fix this defect.
From treating an eye problem to viewing magnified images from microscope, astronomy etc. these defects must be cleared for healthy and precise vision.
Specialized Lens Shapes: Plano-Convex, Biconcave, Meniscus, Aspheric
Lenses are not only simple and single. Various complex forms have been introduced for various special purposes. Some special shapes are as follows:
Plano-convex lens: It is the combination of one flat and the other one curved-outward lens. It is used in laser systems and other devices to focus the collimated beams.
Biconcave lens: It has two inward-curved surfaces. It diverges light and can be used to widen the beam and also to cure myopia in glasses.
Meniscus lenses: These lenses have one concave and one convex surface. It is used to either converge or diverge light depending upon which lens is stronger. They are highly employed in treatment of eyes and fixing spherical aberrations.
Aspheric lenses: These are the reverse to spherical surfaces especially designed to cure spherical aberrations.They are lighter and thinner compared to previous and conventional lenses which are frequently seen in high resolution cameras and correcting lenses.
All these lenses have appropriate use in desired optical devices. Therefore, a right selection of lenses can only give the expected results.
Lens Materials and Refractive Index Choices
Lenses are typically made up of transparent materials like glass or optical plastics which have a definite refractive index. The refractive index guards the bending of light and hence lenses can focus the light at some point. Some major lens components are given below:
- Crown glass having low refractive index diverges light less. Thus, the chance of chromatic aberration is lesser. It is perfect material for simple, single lenses.
- Flint glass has a comparatively higher refractive index and is used in combination with crown glass to produce achromatic aberrations.
- Optical plastics are portable, easier to shape into complicated shapes and are not prone to breaking and hence many optical designs like eyeglasses have replaced the use of expensive glasses. However, they can get scratched easily and are more sensitive to heat.
While selecting a material, every aspect like transparency, longevity, reliability, cost should be considered. For example, germanium or chalcogenide are suitable for infrared glasses but, UV lenses use quartz or fused silica generally. Thus, choosing the right material guarantees the better performance and image quality of the devices.
Magnification, Power, and Field of View Concepts
The important desired outputs from the lenses are: magnification, power, and field of view. These factors also explain how light interacts with the lens to form an image.
Magnification (M) refers to the ratio of imageโs size and objectโs size. It is calculated as:
M = Image height/Object height =v/uโ
Where v is image distance and u is object distance. From the ratio we can conclude that if it is greater than 1 the image is larger than the object and less than 1 means vice-versa.
Power of a lens is an ability of that lens to bend light (converge or diverge). Power is measured in diopters (D) which is also the opposite of focal length.
Power of lens (P) =1/f (in meters)
Convex and concave lenses have positive and negative powers respectively.
Field of View: It is the background area to which a lens can produce an image. In surveillance, telescopes, and cameras, a larger field of view is necessary. To produce a wider field of view, lenses with shorter focal length are used.
Compound Lens Systems and Zoom Mechanisms
Compound lens systems are complex lenses made by merging two or more lenses . This is done to enhance the image quality and performance of a device. They overcome the defects of single lenses, like aberrations, astigmatism etc. For example, in place of simple lenses, biconcave or meniscus lenses are used to treat eye disorders. The combination of crown glass and flint glass reduces chromatic aberrations. In microscopes, objectives contain multiple lenses to provide high magnification with clarity.
A compound system of lenses is employed in cameras to give high resolution and hence increase the image quality called the Zoom lenses. They can continuously provide the variation in wavelength as they can perform tasks like wide-angle and telephoto without swapping the lenses.
There are two types of zooms:
- Optical zooming applies bodily movement to zoom the images and lenses are adjusted physically.
- Digital zoom lowers the resolution of the image by electronically cropping and enlarging the image.
Compound lenses have become the major parts in optical instruments, binoculars, telescopes, and photography today because of their excellent performance, clarity, and flexibility. These instruments require extremely precise results and hence all the requirements are met by those lenses.
Everyday Applications: Cameras, Microscopes, Telescopes, Eyeglasses
We are heavily relying on optical devices today for our everyday activities and advanced works. Some of their important applications are given below:
- Lenses are used in cameras to focus light onto film or an image sensor. Different types of photography demand for different lenses (wide-angle, telephoto, and macro). The lens movement must be accurate to give a right zoom and autofocus.
- The objective and eyepiece lenses used in microscopes produce a magnified view of minute bodies and hence unseen naked-eye details are provided to us. Microbiology or medicine both rely on microscopes to gain a clear, high-magnification image for the purpose of study and diagnostics.
- Telescopes can extract information about distant stars and other celestial bodies by converging light coming from them and hence produce a magnified view of those bodies. The eyepiece lens magnifies the collected image. Refracting telescopes sole;y depend on lenses, while reflecting telescopes use mirrors.
- Eyeglasses are common to us, for viewing objects efficiently. The choice of concave or convex lens depends on the nature of disorder (long-sightedness or short-sightedness). Cylindrical lenses are used to correct astigmatism. Lens are prescribed on the basis of the power needed to treat a patient accurately.
Fiber-Optic and Laser Lenses in Modern Technology
In our modern digital and networking era, fiber-optic and laser lenses are those facilitating us with high-speed communication and precision tasks.
Fiber-optic lenses use optical phenomenon rather than electricity to carry data over a distant connection by focusing and directing light signals between the ends of narrow optical fibers. These lenses provide very high efficiency with almost no signal loss. In fiber optics, gradient-index (GRIN) lenses are widely used to focus light with a refractive index that varies evenly.
All the tasks of laser systems like cuttings, carvings, surgery, and communication are governed by the use of proper compound lenses. To concentrate high-intensity beams, Plano-convex or aspheric lenses are mostly utilized in them to focus the incoming high-intensity beams. Thus, these lenses have to overcome the high power to protect those beams.
Medical lasers are using the LASIK eye surgery method to treat the eye problems which use lenses for its operation. Industrial lasers also employ lenses to cut metals or carve the materials with super accuracy.
Additionally, specialized lenses are also used in beam expanders, collimators, and optical isolators.
Cleaning, Storage, and Maintenance of Optical Lenses
A clean and clear image can be obtained if the source producing it is clear. Therefore, Proper cleaning and maintenance of lenses are required to gain the best performance of a device with clarity. The dust, fingerprints, moisture, scratches and sometimes heat can also degrade the quality of a lens as they are very sensitive materials.
- Cleaning: is done by using a blower that removes loose dust and then it is cleaned with a cleaning lens cleaning solution and a cleaning paper or a microfiber cloth. For delicate lenses (e.g., camera or microscope lenses), special care should be taken while cleaning and using.
- Storage: It is the most important factor that preserves the material from being hampered., corroded or scratched. Ideally, lenses should be kept inside protective cases with silica gel packets to absorb moisture and in dry, dust-free conditions..The coatings or lens material can also be affected by extreme sunlights and temperatures.
- Maintenance tips: Some maintenance ideas for lenses may be using lens caps while not in use, minimizing frequent contact with lens surfaces, and routinely checking lenses for damage. Their coatings are very sensitive, therefore an extra effort can disturb them. Water-resistant and anti-reflective coatings are frequently seen on professional-grade lenses. However, constant optical performance and a long lifespan are guaranteed with routine gentle treatment. and clarity throughout time.
Emerging Innovations: Fresnel, GRIN, and Meta-Lenses
Advancements in optical technology are creating innovative lenses that are thinner, lighter, and more efficient. Three emerging inventions are Fresnel lenses, GRIN lenses, and meta-lenses.
Fresnel lenses: They are invented by Augustin-Jean Fresnel which are flat lenses made of concentric rings. They are very thin and lighter than old lenses but are capable of focusing light efficiently. They are commonly being utilized in lighthouses, overhead projectors, and solar concentrators. Also in modern VR headsets and other compact optics, they are used as they have high precision of image formation.
GRIN (Gradient Index) lenses: They have a refractive index that changes gradually within the material. This gradient bends light smoothly and allows for compact and highly accurate focusing. GRIN lenses are common in fiber-optic systems, compact cameras, and medical instruments.
Meta-lenses are the latest discovery in optics today. They use nanostructured materials inferred to bend light with sub-wavelength precision. The lenses are flat, ultra-thin, and free from traditional aberrations. Meta-lenses have also a solid capability in future to develop mobile phones, AR/VR devices, and compact sensors..
Conclusion
Lenses are like basic needs for optical devices. They regulate light in a desirable way and hence provide us with beautiful and meaningful images. From simple to compound, all magnifying glasses exhibit lenses. However, they are always based on the simple phenomenon of refraction. They have extraordinary ability to bend light and produce magnification.
Every lens has unique features like convex, concave, meniscus, and aspheric as being made from a variety of glass and plastic materials, and have diverse applications like in: spectacles, cameras, microscopes, optical fibres, laser surgeries etc. All these lenses are used for the special purpose of focus, magnification and power.
In this exponentially increasing technological era, Fresnel, GRIN, and meta-lenses are transforming optics and engineering with their size, immense efficiency and functionality. However, the fundamental ideas of refraction, focus, and curvature are still the same for all.
As the sense of vision is a major part of humans, the innovations in the field of optics also makes the vision quality better and scientific. Light and its travelling nature would always be a field of study and research. Hence, the advances in lenses are switching more opportunities for us. (Also read about Dispersion of Light Through Prism)
References
Kingslake, R., & Johnson, R. B. (2009).ย Lens design fundamentals. academic press.
Laikin, M. (2018).ย Lens design. Crc Press.
Hejtmancik, J. F., & Shiels, A. (2015). Overview of the Lens.ย Progress in molecular biology and translational science,ย 134, 119-127.
Pedrotti, F. L., Pedrotti, L. M., & Pedrotti, L. S. (2017).ย Introduction to optics. Cambridge university press.
https://en.wikipedia.org/wiki/Lens
https://www.britannica.com/technology/lens-optics
https://byjus.com/physics/lenses-in-optics/
https://www.sciencing.com/lens-physics-definition-types-how-they-work-13722365/
