The mirror implies a glossy surface at one end and produces an image of an object by reflection. A mirror follows the laws of reflection. The lens is a transparent thick material that is shaped in such a manner that it bends the light passing through it. Answer Expert Verified In converging mirrors light rays at the focus, while In diverging mirror it diverges the rays. Converging mirrors have positive focal length while Diverging mirrors have negative focal length.
Converging mirrors have real focus while Diverging mirrors have virtual focus. Real images may also be inspected by a second lens or lens system. Two sets of rays from common points on an object are reflected by a flat mirror into the eye of an observer.
The reflected rays seem to originate from behind the mirror, locating the virtual image. Now let us consider the focal length of a mirror—for example, the concave spherical mirrors in Figure 2. Rays of light that strike the surface follow the law of reflection.
For a mirror that is large compared with its radius of curvature, as in Figure 2a, we see that the reflected rays do not cross at the same point, and the mirror does not have a well-defined focal point. If the mirror had the shape of a parabola, the rays would all cross at a single point, and the mirror would have a well-defined focal point. But parabolic mirrors are much more expensive to make than spherical mirrors.
The solution is to use a mirror that is small compared with its radius of curvature, as shown in Figure 2b. This is the mirror equivalent of the thin lens approximation. To a very good approximation, this mirror has a well-defined focal point at F that is the focal distance f from the center of the mirror.
The focal length f of a concave mirror is positive, since it is a converging mirror. Figure 2. The distance of the focal point from the center of the mirror is its focal length f.
Since this mirror is converging, it has a positive focal length. A more strongly curved mirror has a shorter focal length and a greater power. The smaller the radius of curvature, the smaller the focal length and, thus, the more powerful the mirror. The convex mirror shown in Figure 3 also has a focal point. Parallel rays of light reflected from the mirror seem to originate from the point F at the focal distance f behind the mirror.
The focal length and power of a convex mirror are negative, since it is a diverging mirror. Ray tracing is as useful for mirrors as for lenses. The rules for ray tracing for mirrors are based on the illustrations just discussed:. Figure 3. Parallel rays of light reflected from a convex spherical mirror small in size compared with its radius of curvature seem to originate from a well-defined focal point at the focal distance f behind the mirror.
Convex mirrors diverge light rays and, thus, have a negative focal length. We will use ray tracing to illustrate how images are formed by mirrors, and we can use ray tracing quantitatively to obtain numerical information. But since we assume each mirror is small compared with its radius of curvature, we can use the thin lens equations for mirrors just as we did for lenses.
Consider the situation shown in Figure 4, concave spherical mirror reflection, in which an object is placed farther from a concave converging mirror than its focal length. Ray tracing in Figure 4 shows that the rays from a common point on the object all cross at a point on the same side of the mirror as the object. Thus a real image can be projected onto a screen placed at this location.
The image distance is positive, and the image is inverted, so its magnification is negative. This is a case 1 image for mirrors. It differs from the case 1 image for lenses only in that the image is on the same side of the mirror as the object.
It is otherwise identical. Figure 4. A case 1 image for a mirror. An object is farther from the converging mirror than its focal length. Rays from a common point on the object are traced using the rules in the text.
Ray 1 approaches parallel to the axis, ray 2 strikes the center of the mirror, and ray 3 goes through the focal point on the way toward the mirror. All three rays cross at the same point after being reflected, locating the inverted real image. Although three rays are shown, only two of the three are needed to locate the image and determine its height. Electric room heaters use a concave mirror to reflect infrared IR radiation from hot coils. Note that IR follows the same law of reflection as visible light.
Given that the mirror has a radius of curvature of The coils are the object, and we are asked to find their location—that is, to find the object distance d o. Assuming the mirror is small compared with its radius of curvature, we can use the thin lens equations, to solve this problem.
You will get the most concentrated thermal energy directly in front of the mirror and 3. Generally, this is not desirable, since it could cause burns. Usually, you want the rays to emerge parallel, and this is accomplished by having the filament at the focal point of the mirror. Note that the filament here is not much farther from the mirror than its focal length and that the image produced is considerably farther away.
This is exactly analogous to a slide projector. Placing a slide only slightly farther away from the projector lens than its focal length produces an image significantly farther away. As the object gets closer to the focal distance, the image gets farther away. In fact, as the object distance approaches the focal length, the image distance approaches infinity and the rays are sent out parallel to one another.
One of the solar technologies used today for generating electricity is a device called a parabolic trough or concentrating collector that concentrates the sunlight onto a blackened pipe that contains a fluid. This heated fluid is pumped to a heat exchanger, where its heat energy is transferred to another system that is used to generate steam—and so generate electricity through a conventional steam cycle.
Figure 5 shows such a working system in southern California. Concave mirrors are used to concentrate the sunlight onto the pipe. The mirror has the approximate shape of a section of a cylinder. For the problem, assume that the mirror is exactly one-quarter of a full cylinder. To solve an Integrated Concept Problem we must first identify the physical principles involved. If the outside of the sphere is silvered such that it can reflect light, then the mirror is said to be convex.
The center of that original sphere is known as the center of curvature C and the line that passes from the mirror's surface through the sphere's center is known as the principal axis. The mirror has a focal point F that is located along the principal axis, midway between the mirror's surface and the center of curvature.
Note that the center of curvature and the focal point are located on the side of the mirror opposite the object - behind the mirror.
Since the focal point is located behind the convex mirror, such a mirror is said to have a negative focal length value. A convex mirror is sometimes referred to as a diverging mirror due to the fact that incident light originating from the same point and will reflect off the mirror surface and diverge.
The diagram at the right shows four incident rays originating from a point and incident towards a convex mirror. These four rays will each reflect according to the law of reflection. After reflection, the light rays diverge; subsequently they will never intersect on the object side of the mirror. For this reason, convex mirrors produce virtual images that are located somewhere behind the mirror. Throughout this unit on Reflection and the Ray Model of Light , the definition of an image has been given.
An image is the location in space where it appears that light diverges from. Any observer from any position who is sighting along a line at the image location will view the object as a result of reflected light. Each observer sees the image in the same location regardless of the observer's location. As the observer sights along a line, a ray of light is reflecting off the mirror to the observer's eye. Thus, the task of determining the image location of an object is to determine the location where reflected light intersects.
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