What type of images are produced by concave mirrors

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. Part 1 is related to the current topic. Part 2 involves a little math, primarily geometry. Part 3 requires an understanding of heat and density. The area for a length of 1.

The mass m of the mineral oil in the one-meter section of pipe is. Figure 5. Parabolic trough collectors are used to generate electricity in southern California. We are considering only one meter of pipe here, and ignoring heat losses along the pipe.

What happens if an object is closer to a concave mirror than its focal length? In fact, this is how makeup mirrors act as magnifiers.

Figure 6a uses ray tracing to locate the image of an object placed close to a concave mirror. Rays from a common point on the object are reflected in such a manner that they appear to be coming from behind the mirror, meaning that the image is virtual and cannot be projected.

As with a magnifying glass, the image is upright and larger than the object. This is a case 2 image for mirrors and is exactly analogous to that for lenses. Figure 6. Ray 1 approaches parallel to the axis, ray 2 strikes the center of the mirror, and ray 3 approaches the mirror as if it came from the focal point.

All three rays appear to originate from the same point after being reflected, locating the upright virtual image behind the mirror and showing it to be larger than the object.

A convex mirror is a diverging mirror f is negative and forms only one type of image. It is a case 3 image—one that is upright and smaller than the object, just as for diverging lenses. Figure 7a uses ray tracing to illustrate the location and size of the case 3 image for mirrors. Since the image is behind the mirror, it cannot be projected and is thus a virtual image. It is also seen to be smaller than the object. Figure 7. Case 3 images for mirrors are formed by any convex mirror.

Ray 1 approaches parallel to the axis, ray 2 strikes the center of the mirror, and ray 3 approaches toward the focal point. All three rays appear to originate from the same point after being reflected, locating the upright virtual image behind the mirror and showing it to be smaller than the object. Because the image is smaller, a larger area is imaged compared to what would be observed for a flat mirror and hence security is improved. A keratometer is a device used to measure the curvature of the cornea, particularly for fitting contact lenses.

Light is reflected from the cornea, which acts like a convex mirror, and the keratometer measures the magnification of the image. The smaller the magnification, the smaller the radius of curvature of the cornea.

If the light source is If we can find the focal length of the convex mirror formed by the cornea, we can find its radius of curvature the radius of curvature is twice the focal length of a spherical mirror. We first solve for the image distance d i , and then for f.

Although the focal length f of a convex mirror is defined to be negative, we take the absolute value to give us a positive value for R. The radius of curvature found here is reasonable for a cornea. An incident ray which strikes the mirror at its vertex is reflected such that its angle of incidence with respect to the principal axis is equal to its angle of reflection.

The validity of these rules in the paraxial approximation is fairly self-evident. Consider an object which is placed a distance from a concave spherical mirror, as shown in Fig.

For the sake of definiteness, let us suppose that the object distance is greater than the focal length of the mirror. Each point on the object is assumed to radiate light-rays in all directions. Consider four light-rays emanating from the tip of the object which strike the mirror, as shown in the figure. The reflected rays are constructed using rules above, and the rays are labelled accordingly. It can be seen that the reflected rays all come together at some point. Thus, is the image of i.

As is easily demonstrated, rays emanating from other parts of the object are brought into focus in the vicinity of such that a complete image of the object is produced between and obviously, point is the image of point.

This image could be viewed by projecting it onto a screen placed between points and. Such an image is termed a real image. Note that the image would also be directly visible to an observer looking straight at the mirror from a distance greater than the image distance since the observer's eyes could not tell that the light-rays diverging from the image were in anyway different from those which would emanate from a real object.

According to the figure, the image is inverted with respect to the object, and is also magnified. Figure Formation of a real image by a concave mirror. Figure 72 shows what happens when the object distance is less than the focal length. In this case, the image appears to an observer looking straight at the mirror to be located behind the mirror. For instance, rays emanating from the tip of the object appear, after reflection from the mirror, to come from a point which is behind the mirror.

Note that only two rays are used to locate , for the sake of clarity. At the center of curvature, the object distance equals the image distance and the object height equals the image height. As the object distance approaches one focal length, the image distance and image height approaches infinity. Finally, when the object distance is equal to exactly one focal length, there is no image. Then altering the object distance to values less than one focal length produces images that are upright, virtual and located on the opposite side of the mirror.

Finally, if the object distance approaches 0, the image distance approaches 0 and the image height ultimately becomes equal to the object height. These patterns are depicted in the diagram below. Nine different object locations are drawn and labeled with a number; the corresponding image locations are drawn in blue and labeled with the identical number.

Compare and contrast the images formed by concave and plane mirrors. Plane mirrors always produce virtual images which are upright and located behind the mirror; they are always the same size as the object.

Concave mirrors can produce both real and virtual images; they can be upright if virtual or inverted if real ; they can be behind the mirror if virtual or in front of the mirror if real ; they can also be enlarged, reduced, or the same size as object. Only a concave mirror can be used to produce a real image; and this only occurs if the object is located at a position of more than one focal length from the concave mirror. A plane mirror will always produce a virtual image. A concave mirror will only produce a virtual image if the object is located in front of the focal point.

A plane mirror will always produce an upright image. A concave mirror will only produce an upright image if the object is located in front of the focal point. Only a concave mirror can be used to produce an inverted image; and this only occurs if the object is located at a position of more than one focal length from the concave mirror.

Real images can be larger than the object, smaller than the object, or the same size as the object. The famous Chinese magician, Foo Ling Yu, conducts a classic magic trick utilizing a concave mirror with a focal length of 1. Foo Ling Yu is able to use the mirror in such a manner as to produce an image of a light bulb at the same location and of the same size as the actual light bulb itself.

Use complete sentences to explain how Foo is able to accomplish this magic trick. Be specific about the light bulb location. Foo Ling Yu has probably placed the object at the center of curvature - a distance of 3. When Foo does this, a real image is formed at the same location and of the same size. Physics Tutorial. My Cart Subscription Selection. Student Extras. Watch It! We Would Like to Suggest Why just read about it and when you could be interacting with it?