Concave and Convex
Concave and convex refer to two types of lens shapes that manipulate light in distinct ways. Concave lenses are diverging lenses that spread light rays apart, creating images that seem to originate from a point in front of the lens. This property is utilized in applications such as correcting nearsightedness, allowing distant objects to appear clearer. Conversely, convex lenses are converging lenses that focus light rays to a point, producing images that are magnified. They are commonly found in devices like cameras and telescopes, where focusing light onto a detector is essential for forming clear images.
The study of optics, which includes the behavior of light through these lenses, has significantly advanced through historical contributions from scientists like Galileo and Newton. Understanding how light refracts and reflects is critical in various fields, from astronomy to modern technology, including the production of microchips and advanced imaging devices. The principles of light manipulation through lenses and mirrors continue to play a crucial role in everyday life and scientific exploration.
Concave and Convex
FIELDS OF STUDY: Optics; Electromagnetism
ABSTRACT: Mirrors and lenses have been instrumental in the development of science and society over the course of history. These devices have been used in military, scientific, and biological applications for thousands of years. This article explains the laws and properties that make these uses possible.
Principal Terms
- converging: the joining of light rays after an interaction with a mirror or a lens.
- diverging: the separation of light rays after an interaction with a mirror or a lens.
- focal point: the place where light from a source converges after it reflects off a mirror or refracts through a lens.
- inversion: the reversal of the way an image looks after an interaction with a mirror or lens.
- refraction: the bending of the direction of light when it goes from one substance to another.
- reflection: the bouncing of light with an angle equal to the angle at which it first comes in contact with an object.
- Snell’s law: a mathematical description of the refraction of light as it goes from one medium to another.
The Study of Optics
One of the most important fields of physics is the study of light and optical instruments. These instruments have provided a vast understanding of different kinds of phenomena and objects. With his knowledge and understanding of optical instruments, Galileo Galilei (1564–1642), for example, created a telescope that led him to observe the moons of Jupiter, sunspots, and other astronomical occurrences.
Optical instruments have advanced science in the microscopic realm as well. For example, through his use of the compound microscope, Robert Hooke (1635–1703) was able to describe and name the cell for the first time. With the help of optical instruments, other scientists have been able to develop theories of genes and microbes, instrumental in the detection and control of diseases.
Furthermore, Isaac Newton (1642–1727) developed and built the first useful reflecting telescope. In turn, the Newtonian telescope led to advancements in the development of other reflecting telescopes. Newton used a mirror instead of a lens, focusing light through the use of reflection. Before the Newtonian telescope, telescopes used lenses, which are refractors. They used the property of refraction through a lens to focus light.
Focusing Light
Many different techniques have been employed to focus light into a point. Originally, opticians preferred lenses to mirrors because the process of making them was easier. Two different kinds of lenses were produced: converging, or convex lenses, and diverging, or concave lenses. Converging lenses let light through and focus it past the lens. These lenses converge the light to a point where the image forms. Most camera lenses are converging lenses. They have to focus the light into the detector (a film or sensor), the focal point in a camera.
Diverging, or concave, lenses, on the other hand, refract the light in such a way that it spreads apart on the other side of the lens. These lenses create images that appear to have come from in front of the lens. This is useful in the creation of holograms and in the correction of nearsighted vision. When a nearsighted person puts a diverging lens in front of his or her eyes, far-away images appear closer. These images are picked up by the eye. Since the images are closer, the person is able to see them clearly.
In the same manner, a converging lens can be used to correct farsightedness. In this case, the lens makes objects appear to be farther away than they are. These methods can fix these two eye conditions by using basic principles of physics.
When light passes from one substance to another, its speed changes slightly, and it is bent or directed in a slightly different direction. Different substances react differently to light going through them. Some slow down light more than others do. The slowing of light compared to the speed of light in a vacuum is quantified in the constant called "index of refraction" (n). The bending of the path of light depends on the angle from which the light comes (θ1), the angle at which the light emerges (θ2), and the index of refraction of each substance (n1 and n2, respectively). This is known as Snell’s law. It follows the mathematical formula
n1 sin θ1 = n2 sin θ2
The angles θ1 and θ2 are measured with respect to the line perpendicular to the boundary between the two substances. Imagine light from the sun hits the surface of a pool at an initial (or incidence) angle (θ1) of 30 degrees. The index of refraction of air (n1) is 1. The index of refraction of water (n2) is 1.33. To calculate the angle of refraction (θ2), substitute these values into the formula for Snell’s law, as below.
From Lenses to Mirrors
After many advancements in glassmaking, mirrors became easier to make. In 1668, Newton completed the first successful reflecting telescope. Instead of using lenses in his telescope, Newton focused the light with a converging, or concave, mirror. The secondary mirror in telescopes can be diverging, as it sends the light back without inverting it. It also allows for a wider field of view. Mirrors follow a much simpler optical rule than lenses do. The angle of incidence (θi) equals the angle of reflection (θf):
θi = θf
Both plane and curved mirrors invert images through image inversion. When looking at the moon through a telescope people might notice that the image is inverted. What looks like the left side of the moon in the telescope is actually the right side. The same effect happens when one looks at oneself on a concave mirror or through a convex lens. This occurs because mirrors reflect light in the same direction they receive it, while lenses refract light that goes through them.
Daily Use of Mirrors and Lenses
The industry of glassmaking has existed for millennia. From the glass beads found on King Tut’s body to the legendary glassmakers of Venice and the modern makers of telescope mirrors and lenses, mirrors and lenses have been essential parts of everyone’s life. Without these developments nearsighted and farsighted people would not be able to see the world around them clearly. The technology industry also depends heavily on mirrors to make microchips. Curved televisions, monitors, and other devices are becoming popular because of the advancements in mirror- and glassmaking. Future discoveries in physics and astrophysics will rely on both large mirrors and those that can reflect infrared and other forms of light.
Bibliography
Breinig, Marianne. "Reflection and Refraction." Elements of Physics II. U of Tennessee, Dept. of Physics and Astronomy, n.d. Web. 6 May 2015.
Conrady, A. E. Applied Optics and Optical Design. Newburyport: Dover, 2013. Print.
Giambattista, Alan, and Betty McCarthy Richardson. Physics. 3rd ed. New York: McGraw, 2015. Print.
Nave, R. "Refraction of Light." HyperPhysics. Dept. of Physics and Astronomy, Georgia State U, n.d. Web. 6 May 2015.
Rasmussen, Seth C. How Glass Changed the World: The History and Chemistry of Glass from Antiquity to the Thirteenth Century. New York: Springer, 2012. Print.
Young, Hugh D., Philip W. Adams, and Raymond J. Chastain. Sears and Zemansky’s College Physics. 10th ed. Hoboken: Pearson, 2016. Print.