Magnification
Magnification refers to the process of enlarging the appearance of an object, allowing details to be observed that might not be visible to the naked eye. It is commonly achieved using optical devices such as lenses and mirrors, which manipulate light to produce images that vary in size and clarity. Two key types of magnification are linear magnification, which compares the apparent height of a magnified image to the actual height of the object, and angular magnification, which assesses the angle subtended by the magnified image at the eye versus the angle of the object viewed without magnification.
Lenses can be categorized as convex, concave, or flat, each influencing the resulting image differently. For instance, convex lenses converge light rays, producing larger images, while concave lenses cause light rays to diverge, creating virtual images. Mirrors, on the other hand, reflect light, with concave mirrors producing smaller images and convex mirrors producing larger virtual images.
Magnification is utilized in various modern devices, including cameras, telescopes, and microscopes, enhancing our ability to observe and study both distant and minute objects. Understanding magnification also involves grasping related concepts such as reflection, refraction, and resolution, which are crucial in determining image clarity and detail.
Magnification
FIELDS OF STUDY: Optics; Spectroscopy
ABSTRACT: The properties of mirrors and lenses are used to magnify objects. Magnification creates an enlarged image of an object. Various lenses can cause light rays to converge or diverge. Magnification is a basic principle of optical devices, such as cameras, telescopes, microscopes, and projectors.
PRINCIPAL TERMS
- angular magnification: the angle subtended at the eye by a magnified image of an object divided by the angle of the object being viewed by the naked eye without magnification.
- concave: having surfaces that curve inward, like a bowl.
- convex: having surfaces that curve outward, like a ball.
- focal length: the distance from the center of a lens or mirror to the focal point, where transmitted or reflected light rays converge.
- linear magnification: the ratio of the apparent height of an object’s magnified image to the actual height of the object.
- resolution: the smallest identifiable dimension that a lens can differentiate.
- transverse magnification: also known as lateral magnification; synonymous with linear magnification.
- virtual image: an image that forms at the point where the paths of rays cross when projected backward from a lens.
Lenses and Mirrors
Lenses transmit light and are capable of reproducing an image. Mirrors reflect light and are capable of reproducing or distorting an image. A flat mirror reflects light back to an observer. Observers see a virtual image produced by the reflected light as if they were seeing the reflected object behind the mirror. The virtual image seen in a flat mirror cannot be projected onto another surface because the light rays do not pass through the perceived image. Mirrors can also magnify or reduce an image, depending on the shape of their reflective surface. A concave mirror has a reflective surface that curves inward. A convex mirror has a reflective surface that curves outward. Concave mirrors distort the virtual image to make it appear smaller than the actual object. Convex mirrors distort the virtual image to make it appear larger. In a flat mirror, the dimensions of the virtual image and the dimensions of the object are the same. Magnification is the ratio of the image dimensions to the object dimensions. Therefore, the images reflected by a flat mirror have a magnification of 1. Images reflected by a concave mirror have a negative magnification, and images reflected by a convex mirror have a positive magnification.
If one thinks of a concave or convex mirror as being one section of a circle, the center point of that circle is called the center of curvature. The principal axis of that circle would intersect the mirror at a point known as the vertex. The distance from the vertex to the center of curvature is known as the radius of curvature. The midway point between the vertex and the center of curvature is called the focal point. The distance from the vertex to the focal point is called the focal length. The focal length of a lens describes how strongly it converges or diverges light. The index of refraction is the ratio of the speed of light in a vacuum to its speed in a material. The focal length of a lens is determined by the material’s index of refraction, that of air, the radius of curvature for the incoming side of the lens, and the radius of curvature for the outgoing side.
Lenses are also described as convex, concave, or flat. When parallel light rays pass through a lens, they may either converge to a single point beyond the lens or appear to diverge from a single point in front of the lens. The most important function of a lens is magnification. When light passes through a double convex lens, the light rays are refracted by the lens material and change direction according to the material’s index of refraction. When the light rays pass through the opposite surface of the lens, they are refracted again and converge at a single focal point on the other side of the lens. Parallel rays traveling through a double concave lens refract from the lens and diverge, never intersecting on the other side of the lens. Thus, they appear to diverge from a single point in front of the lens. For a flat lens, such as the glass in a window, the light rays pass directly through and emerge parallel.
Lenses and Magnification
Lens shape determines how the image the lens produces will be magnified. A simple magnifying glass uses a single convex lens to produce an image that is larger than the object itself. The ratio of the apparent size of the image to the actual size of the object at the focal length of the lens determines the linear magnification (also known as transverse magnification or lateral magnification). An inverted image has a negative value of linear magnification. The angular magnification of a lens or system of lenses denotes the angle between the observer’s line of sight and the bottom of the object and the same point in its image.
A concave lens produces a virtual image at the focal length of its curved surface. Light rays passing through a concave lens spread apart, or diverge. Concave and convex lenses can be combined in a complementary fashion so that the image from one lens becomes magnified by other lenses. This is the basic operating principle of binoculars, telescopes, and microscopes, and can achieve large degrees of magnification. Cameras and projectors also depend on this function. In cameras, light enters through a system of lenses and is directed to a light-sensitive surface, such as photographic film or the electronic sensors used in digital cameras. In projectors, light is projected through the image and on through a system of lenses to a surface where it can be seen in a much enlarged format. Typically, the image becomes inverted as the light passes through the focal point.
Sample Problem
A coin has a diameter of 1.27 centimeters (0.5 inches). When examined with a simple magnifying glass it appears much larger, and the largest image is seen when the coin and the observer's eye are both at the focal length of the lens, a distance of 25.4 centimeters (10 inches). Using a ruler on the face of the lens, the coin appears to be 5.6 centimeters (2.2 inches) in diameter. What is the magnification of the lens?
Answer:
The actual image is 1.27 centimeters (0.5 inches) in diameter (d), and the virtual image is 5.6 centimeters (2.2 inches). The linear magnification is the ratio of the apparent size of the virtual image to the size of the real object.
dvirtual / dreal = 5.6 cm / 1.27 cm = 4.4
Therefore, the lens has a magnifying power of 4.4, indicating that it can make objects appear 4.4 times larger.
Reflection, Refraction, and Diffraction
Reflection involves a change in the direction as light rays bounce off the surface of a mirror. Light waves follow the law of reflection: the incident angle, or the angle at which the light approaches the mirror, is equal to the angle of reflection. Refraction and diffraction can affect light as it passes from one medium to another. Diffraction results in a change in the direction of light rays as they pass through an opening or encounter an obstacle. Diffraction can separate light rays according to frequency. One effect of diffraction is the rainbow, in which bands of different colors appear as white light from the sun is separated into different visible wavelengths. Because the focal lengths for different wavelengths of light differ slightly, diffraction can cause a chromatic aberration. Chromatic aberrations can be seen as colored halos around the image in the lens. This effect can make fine details difficult or impossible to see.
The dimension of the smallest detail that can be seen clearly through a magnifying lens determines the resolution of the lens. Typically, the greater the magnifying power of the lens is, the finer its resolution is, as it enables ever smaller details to be seen. Resolution is limited by chromatic aberration and distortions due to refraction and reflection. At each surface of the lens, a certain amount of the light is reflected rather than transmitted. Reflection within the lens material actually produces two images rather than just one image, separated by a distance determined by the thickness of the lens. This can be seen by carefully examining the edge of a reflection in a mirror, where two reflections will actually be seen. The clearest image is obtained at the average focal length of the two surfaces and is termed the circle of least confusion.
Bibliography
Darrigol, Olivier. A History of Optics from Greek Antiquity to the Nineteenth Century. New York: Oxford UP, 2012. Print.
Ghatak, Ajoy. Optics. 3rd ed. New Delhi: Tata McGraw-Hill, 2005. Print.
Sharma, K. K. Optics Principles and Applications. Burlington: Academic, 2006. Print.
Ersoy, Okan K. Diffraction, Fourier Optics and Imaging. Hoboken: Wiley, 2007. Print.
Laikin, Milton. Lens Design. 4th ed. Boca Raton: CRC, 2007. Print.
Duree, Galen, Jr. Optics for Dummies. Hoboken: Wiley, 2011. Print.